diff --git a/CMakeLists.txt b/CMakeLists.txt
index 6b4f0a54d493750762038fb9ca4230b4293f5655..dc0f693980d6771d005c961cfae8f023ae81d174 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -139,8 +139,16 @@ endif()
 
 #------------------------------------------------------
 # Check for PETSc
-find_package(PETSc)
-set(PUGS_HAS_PETSC ${PETSC_FOUND})
+# defaults use PETSc
+set(PUGS_ENABLE_PETSC AUTO CACHE STRING
+  "Choose one of: AUTO ON OFF")
+
+if (PUGS_ENABLE_PETSC MATCHES "^(AUTO|ON)$")
+  find_package(PETSc)
+  set(PUGS_HAS_PETSC ${PETSC_FOUND})
+else()
+  unset(PUGS_HAS_PETSC)
+endif()
 
 if (${PETSC_FOUND})
   include_directories(SYSTEM ${PETSC_INCLUDES})
@@ -474,14 +482,22 @@ else()
   if(NOT PARMETIS_LIBRARIES)
     message(" MPI: deactivated: ParMETIS cannot be found!")
   else()
-    message(" MPI: not found!")
+    if (PUGS_ENABLE_MPI MATCHES "^(AUTO|ON)$")
+      message(" MPI: not found!")
+    else()
+      message(" MPI: explicitly deactivated!")
+    endif()
   endif()
 endif()
 
 if (PETSC_FOUND)
   message(" PETSc: ${PETSC_VERSION}")
 else()
-  message(" PETSc: not found!")
+  if (PUGS_ENABLE_PETSC MATCHES "^(AUTO|ON)$")
+    message(" PETSc: not found!")
+  else()
+      message(" PETSc: explicitly deactivated!")
+  endif()
 endif()
 
 if(CLANG_FORMAT)
diff --git a/src/algebra/BiCGStab.hpp b/src/algebra/BiCGStab.hpp
index bc822668a7f63c4d5d7cc4c45f4d1b1d70084fc0..ff34b89e148d844215cf7fffc21c2ad78bca5ec9 100644
--- a/src/algebra/BiCGStab.hpp
+++ b/src/algebra/BiCGStab.hpp
@@ -7,16 +7,20 @@
 
 #include <rang.hpp>
 
-template <bool verbose = true>
 struct BiCGStab
 {
   template <typename VectorType, typename MatrixType>
-  BiCGStab(const VectorType& b, const MatrixType& A, VectorType& x, const size_t max_iter, const double epsilon = 1e-6)
+  BiCGStab(const MatrixType& A,
+           VectorType& x,
+           const VectorType& b,
+           const double epsilon,
+           const size_t maximum_iteration,
+           const bool verbose)
   {
-    if constexpr (verbose) {
+    if (verbose) {
       std::cout << "- bi-conjugate gradient stabilized\n";
       std::cout << "  epsilon = " << epsilon << '\n';
-      std::cout << "  maximum number of iterations: " << max_iter << '\n';
+      std::cout << "  maximum number of iterations: " << maximum_iteration << '\n';
     }
 
     VectorType r_k_1{b.size()};
@@ -38,13 +42,13 @@ struct BiCGStab
 
       VectorType r_k{x.size()};
 
-      if constexpr (verbose) {
+      if (verbose) {
         std::cout << "   initial residu: " << resid0 << '\n';
       }
-      for (size_t i = 1; i <= max_iter; ++i) {
-        if constexpr (verbose) {
-          std::cout << "  - iteration: " << std::setw(6) << i << "\tresidu: " << residu / resid0
-                    << "\tabsolute: " << residu << '\n';
+      for (size_t i = 1; i <= maximum_iteration; ++i) {
+        if (verbose) {
+          std::cout << "  - iteration: " << std::setw(6) << i << " residu: " << std::scientific << residu / resid0
+                    << " absolute: " << std::scientific << residu << '\n';
         }
 
         Ap_k = A * p_k;
@@ -77,8 +81,8 @@ struct BiCGStab
                   << '\n';
         ;
         std::cout << "  - epsilon:          " << epsilon << '\n';
-        std::cout << "  - relative residu : " << residu / resid0 << '\n';
-        std::cout << "  - absolute residu : " << residu << '\n';
+        std::cout << "  - relative residu : " << std::scientific << residu / resid0 << '\n';
+        std::cout << "  - absolute residu : " << std::scientific << residu << '\n';
       }
     }
   }
diff --git a/src/algebra/PCG.hpp b/src/algebra/CG.hpp
similarity index 60%
rename from src/algebra/PCG.hpp
rename to src/algebra/CG.hpp
index 36a4635b313d2bba13d97e1b7a4ea1882e2a66a2..538c77571dac4d551d7476ea79bf855e8026fb53 100644
--- a/src/algebra/PCG.hpp
+++ b/src/algebra/CG.hpp
@@ -6,30 +6,30 @@
 
 #include <rang.hpp>
 
-template <bool verbose = true>
-struct PCG
+struct CG
 {
-  template <typename VectorType, typename MatrixType, typename PreconditionerType>
-  PCG(const VectorType& f,
-      const MatrixType& A,
-      [[maybe_unused]] const PreconditionerType& C,
-      VectorType& x,
-      const size_t maxiter,
-      const double epsilon = 1e-6)
+  template <typename VectorType, typename MatrixType>
+  CG(const MatrixType& A,
+     VectorType& x,
+     const VectorType& f,
+     const double epsilon,
+     const size_t maximum_iteration,
+     const bool verbose = false)
   {
-    if constexpr (verbose) {
+    if (verbose) {
       std::cout << "- conjugate gradient\n";
       std::cout << "  epsilon = " << epsilon << '\n';
-      std::cout << "  maximum number of iterations: " << maxiter << '\n';
+      std::cout << "  maximum number of iterations: " << maximum_iteration << '\n';
     }
 
     VectorType h{f.size()};
     VectorType b = copy(f);
 
-    if constexpr (verbose) {
+    if (verbose) {
       h = A * x;
       h -= f;
-      std::cout << "- initial *real* residu :   " << (h, h) << '\n';
+      std::cout << "- initial " << rang::style::bold << "real" << rang::style::reset << " residu :   " << (h, h)
+                << '\n';
     }
 
     VectorType g{b.size()};
@@ -40,7 +40,7 @@ struct PCG
 
     double relativeEpsilon = epsilon;
 
-    for (size_t i = 1; i <= maxiter; ++i) {
+    for (size_t i = 1; i <= maximum_iteration; ++i) {
       if (i == 1) {
         h = A * x;
 
@@ -74,13 +74,13 @@ struct PCG
       if ((i == 1) && (gcg != 0)) {
         relativeEpsilon = epsilon * gcg;
         gcg0            = gcg;
-        if constexpr (verbose) {
+        if (verbose) {
           std::cout << "  initial residu: " << gcg << '\n';
         }
       }
-      if constexpr (verbose) {
-        std::cout << "  - iteration " << std::setw(6) << i << "\tresidu: " << gcg / gcg0;
-        std::cout << "\tabsolute: " << gcg << '\n';
+      if (verbose) {
+        std::cout << "  - iteration " << std::setw(6) << i << std::scientific << " residu: " << gcg / gcg0;
+        std::cout << " absolute: " << std::scientific << gcg << '\n';
       }
 
       if (gcg < relativeEpsilon) {
@@ -96,8 +96,8 @@ struct PCG
     if (gcg > relativeEpsilon) {
       std::cout << "  conjugate gradient: " << rang::fgB::red << "*NOT CONVERGED*" << rang::style::reset << '\n';
       std::cout << "  - epsilon:          " << epsilon << '\n';
-      std::cout << "  - relative residu : " << gcg / gcg0 << '\n';
-      std::cout << "  - absolute residu : " << gcg << '\n';
+      std::cout << "  - relative residu : " << std::scientific << gcg / gcg0 << '\n';
+      std::cout << "  - absolute residu : " << std::scientific << gcg << '\n';
     }
   }
 };
diff --git a/src/algebra/CMakeLists.txt b/src/algebra/CMakeLists.txt
index bbd2d01bf417baaacb13c6c7362a825337a180be..d1f01ec310858be0e775514f934ce0a7c0e9da28 100644
--- a/src/algebra/CMakeLists.txt
+++ b/src/algebra/CMakeLists.txt
@@ -2,5 +2,6 @@
 
 add_library(
   PugsAlgebra
-  LinearSystemSolver.cpp
+  LinearSolver.cpp
+  LinearSolverOptions.cpp
   PETScWrapper.cpp)
diff --git a/src/algebra/CRSMatrix.hpp b/src/algebra/CRSMatrix.hpp
index 97a0a8a8ed44d660f9524eac269abee0324cd136..d9b03ac93fb2f1c4baeff98c90daac17547ff7cf 100644
--- a/src/algebra/CRSMatrix.hpp
+++ b/src/algebra/CRSMatrix.hpp
@@ -30,8 +30,21 @@ class CRSMatrix
     return m_host_matrix.numRows();
   }
 
+  auto
+  values() const
+  {
+    return m_values;
+  }
+
+  auto
+  hostMatrix() const
+  {
+    return m_host_matrix;
+  }
+
   template <typename DataType2>
-  Vector<MutableDataType> operator*(const Vector<DataType2>& x) const
+  Vector<MutableDataType>
+  operator*(const Vector<DataType2>& x) const
   {
     static_assert(std::is_same<std::remove_const_t<DataType>, std::remove_const_t<DataType2>>(),
                   "Cannot multiply matrix and vector of different type");
diff --git a/src/algebra/LinearSolver.cpp b/src/algebra/LinearSolver.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..a275cd5816d6ce04715fd1d160008b4dd8508051
--- /dev/null
+++ b/src/algebra/LinearSolver.cpp
@@ -0,0 +1,320 @@
+#include <algebra/LinearSolver.hpp>
+#include <utils/pugs_config.hpp>
+
+#include <algebra/BiCGStab.hpp>
+#include <algebra/CG.hpp>
+
+#ifdef PUGS_HAS_PETSC
+#include <petsc.h>
+#endif   // PUGS_HAS_PETSC
+
+struct LinearSolver::Internals
+{
+  static bool
+  hasLibrary(const LSLibrary library)
+  {
+    switch (library) {
+    case LSLibrary::builtin: {
+      return true;
+    }
+    case LSLibrary::petsc: {
+#ifdef PUGS_HAS_PETSC
+      return true;
+#else
+      return false;
+#endif
+    }
+    default: {
+      throw UnexpectedError("Linear system library (" + ::name(library) + ") was not set!");
+    }
+    }
+  }
+
+  static void
+  checkHasLibrary(const LSLibrary library)
+  {
+    if (not hasLibrary(library)) {
+      throw NormalError(::name(library) + " is not linked to pugs. Cannot use it!");
+    }
+  }
+
+  static void
+  checkBuiltinMethod(const LSMethod method)
+  {
+    switch (method) {
+    case LSMethod::cg:
+    case LSMethod::bicgstab: {
+      break;
+    }
+    default: {
+      throw NormalError(name(method) + " is not a builtin linear solver!");
+    }
+    }
+  }
+
+  static void
+  checkPETScMethod(const LSMethod method)
+  {
+    switch (method) {
+    case LSMethod::cg:
+    case LSMethod::bicgstab:
+    case LSMethod::bicgstab2:
+    case LSMethod::gmres:
+    case LSMethod::lu:
+    case LSMethod::choleski: {
+      break;
+    }
+    default: {
+      throw NormalError(name(method) + " is not a builtin linear solver!");
+    }
+    }
+  }
+
+  static void
+  checkBuiltinPrecond(const LSPrecond precond)
+  {
+    switch (precond) {
+    case LSPrecond::none: {
+      break;
+    }
+    default: {
+      throw NormalError(name(precond) + " is not a builtin preconditioner!");
+    }
+    }
+  }
+
+  static void
+  checkPETScPrecond(const LSPrecond precond)
+  {
+    switch (precond) {
+    case LSPrecond::none:
+    case LSPrecond::diagonal:
+    case LSPrecond::incomplete_choleski:
+    case LSPrecond::incomplete_LU: {
+      break;
+    }
+    default: {
+      throw NormalError(name(precond) + " is not a PETSc preconditioner!");
+    }
+    }
+  }
+
+  static void
+  checkOptions(const LinearSolverOptions& options)
+  {
+    switch (options.library()) {
+    case LSLibrary::builtin: {
+      checkBuiltinMethod(options.method());
+      checkBuiltinPrecond(options.precond());
+      break;
+    }
+    case LSLibrary::petsc: {
+      checkPETScMethod(options.method());
+      checkPETScPrecond(options.precond());
+      break;
+    }
+    default: {
+      throw UnexpectedError("undefined options compatibility for this library (" + ::name(options.library()) + ")!");
+    }
+    }
+  }
+
+  static void
+  builtinSolveLocalSystem(const CRSMatrix<double, size_t>& A,
+                          Vector<double>& x,
+                          const Vector<double>& b,
+                          const LinearSolverOptions& options)
+  {
+    if (options.precond() != LSPrecond::none) {
+      throw UnexpectedError("builtin linear solver do not allow any preconditioner!");
+    }
+    switch (options.method()) {
+    case LSMethod::cg: {
+      CG{A, x, b, options.epsilon(), options.maximumIteration(), options.verbose()};
+      break;
+    }
+    case LSMethod::bicgstab: {
+      BiCGStab{A, x, b, options.epsilon(), options.maximumIteration(), options.verbose()};
+      break;
+    }
+    default: {
+      throw NotImplementedError("undefined builtin method: " + name(options.method()));
+    }
+    }
+  }
+
+#ifdef PUGS_HAS_PETSC
+
+  static int
+  petscMonitor(KSP, int i, double residu, void*)
+  {
+    std::cout << "  - iteration: " << std::setw(6) << i << " residu: " << std::scientific << residu << '\n';
+    return 0;
+  }
+
+  static void
+  petscSolveLocalSystem(const CRSMatrix<double, size_t>& A,
+                        Vector<double>& x,
+                        const Vector<double>& b,
+                        const LinearSolverOptions& options)
+  {
+    Assert(x.size() == b.size() and x.size() == A.numberOfRows());
+
+    Vec petscB;
+    VecCreateMPIWithArray(PETSC_COMM_WORLD, 1, b.size(), b.size(), &b[0], &petscB);
+    Vec petscX;
+    VecCreateMPIWithArray(PETSC_COMM_WORLD, 1, x.size(), x.size(), &x[0], &petscX);
+
+    Mat petscMat;
+    MatCreate(PETSC_COMM_WORLD, &petscMat);
+    MatSetSizes(petscMat, PETSC_DECIDE, PETSC_DECIDE, x.size(), x.size());
+
+    MatSetType(petscMat, MATAIJ);
+
+    Array<PetscScalar> values = copy(A.values());
+    auto hm                   = A.hostMatrix();
+
+    Array<PetscInt> row_indices{hm.row_map.size()};
+    for (size_t i = 0; i < hm.row_map.size(); ++i) {
+      row_indices[i] = hm.row_map[i];
+    }
+
+    Array<PetscInt> column_indices{values.size()};
+    size_t l = 0;
+    for (size_t i = 0; i < A.numberOfRows(); ++i) {
+      const auto row_i = hm.rowConst(i);
+      for (size_t j = 0; j < row_i.length; ++j) {
+        column_indices[l++] = row_i.colidx(j);
+      }
+    }
+
+    MatCreateSeqAIJWithArrays(PETSC_COMM_WORLD, x.size(), x.size(), &row_indices[0], &column_indices[0], &values[0],
+                              &petscMat);
+
+    MatAssemblyBegin(petscMat, MAT_FINAL_ASSEMBLY);
+    MatAssemblyEnd(petscMat, MAT_FINAL_ASSEMBLY);
+
+    KSP ksp;
+    KSPCreate(PETSC_COMM_WORLD, &ksp);
+    KSPSetTolerances(ksp, options.epsilon(), 1E-100, 1E5, options.maximumIteration());
+
+    KSPSetOperators(ksp, petscMat, petscMat);
+
+    PC pc;
+    KSPGetPC(ksp, &pc);
+
+    bool direct_solver = false;
+
+    switch (options.method()) {
+    case LSMethod::bicgstab: {
+      KSPSetType(ksp, KSPBCGS);
+      break;
+    }
+    case LSMethod::bicgstab2: {
+      KSPSetType(ksp, KSPBCGSL);
+      KSPBCGSLSetEll(ksp, 2);
+      break;
+    }
+    case LSMethod::cg: {
+      KSPSetType(ksp, KSPCG);
+      break;
+    }
+    case LSMethod::gmres: {
+      KSPSetType(ksp, KSPGMRES);
+
+      break;
+    }
+    case LSMethod::lu: {
+      KSPSetType(ksp, KSPPREONLY);
+      PCSetType(pc, PCLU);
+      PCFactorSetShiftType(pc, MAT_SHIFT_NONZERO);
+      direct_solver = true;
+      break;
+    }
+    case LSMethod::choleski: {
+      KSPSetType(ksp, KSPPREONLY);
+      PCSetType(pc, PCCHOLESKY);
+      direct_solver = true;
+      break;
+    }
+    default: {
+      throw UnexpectedError("unexpected method: " + name(options.method()));
+    }
+    }
+
+    if (not direct_solver) {
+      switch (options.precond()) {
+      case LSPrecond::diagonal: {
+        PCSetType(pc, PCJACOBI);
+        break;
+      }
+      case LSPrecond::incomplete_LU: {
+        PCSetType(pc, PCILU);
+        break;
+      }
+      case LSPrecond::incomplete_choleski: {
+        PCSetType(pc, PCICC);
+        break;
+      }
+      case LSPrecond::none: {
+        PCSetType(pc, PCNONE);
+        break;
+      }
+      default: {
+        throw UnexpectedError("unexpected preconditioner: " + name(options.precond()));
+      }
+      }
+    }
+    if (options.verbose()) {
+      KSPMonitorSet(ksp, petscMonitor, 0, 0);
+    }
+
+    KSPSolve(ksp, petscB, petscX);
+    MatDestroy(&petscMat);
+  }
+
+#else
+  static void
+  petscSolveLocalSystem(const CRSMatrix<double, size_t>&,
+                        Vector<double>&,
+                        const Vector<double>&,
+                        const LinearSolverOptions&)
+  {
+    checkHasLibrary(LSLibrary::petsc);
+    throw UnexpectedError("unexpected situation should not reach this point!");
+  }
+
+#endif   // PUGS_HAS_PETSC
+};
+
+bool
+LinearSolver::hasLibrary(LSLibrary library) const
+{
+  return Internals::hasLibrary(library);
+}
+
+void
+LinearSolver::solveLocalSystem(const CRSMatrix<double, size_t>& A, Vector<double>& x, const Vector<double>& b)
+{
+  switch (m_options.library()) {
+  case LSLibrary::builtin: {
+    Internals::builtinSolveLocalSystem(A, x, b, m_options);
+    break;
+  }
+  case LSLibrary::petsc: {
+    Internals::petscSolveLocalSystem(A, x, b, m_options);
+    break;
+  }
+  default: {
+    throw UnexpectedError(::name(m_options.library()) + " cannot solve local systems for sparse matrices");
+  }
+  }
+}
+
+LinearSolver::LinearSolver(const LinearSolverOptions& options) : m_options{options}
+{
+  Internals::checkHasLibrary(m_options.library());
+  Internals::checkOptions(options);
+}
+
+LinearSolver::LinearSolver() : LinearSolver{LinearSolverOptions::default_options} {}
diff --git a/src/algebra/LinearSolver.hpp b/src/algebra/LinearSolver.hpp
new file mode 100644
index 0000000000000000000000000000000000000000..b72b09b0f6a3255f914c96ee3df7717923931294
--- /dev/null
+++ b/src/algebra/LinearSolver.hpp
@@ -0,0 +1,36 @@
+#ifndef LINEAR_SOLVER_HPP
+#define LINEAR_SOLVER_HPP
+
+#include <algebra/CRSMatrix.hpp>
+#include <algebra/LinearSolverOptions.hpp>
+#include <algebra/TinyMatrix.hpp>
+#include <algebra/TinyVector.hpp>
+#include <algebra/Vector.hpp>
+#include <utils/Exceptions.hpp>
+
+class LinearSolver
+{
+ private:
+  struct Internals;
+
+  const LinearSolverOptions m_options;
+
+  void _solveLocalDense(size_t N, const double* A, double* x, const double* b);
+
+ public:
+  bool hasLibrary(LSLibrary library) const;
+
+  void solveLocalSystem(const CRSMatrix<double, size_t>& A, Vector<double>& x, const Vector<double>& b);
+
+  template <size_t N>
+  void
+  solveLocalSystem(const TinyMatrix<N>& A, TinyVector<N>& x, const TinyVector<N>& b)
+  {
+    this->_solveLocalDense(N, &A(0, 0), &x[0], &b[0]);
+  }
+
+  LinearSolver();
+  LinearSolver(const LinearSolverOptions& options);
+};
+
+#endif   // LINEAR_SOLVER_HPP
diff --git a/src/algebra/LinearSolverOptions.cpp b/src/algebra/LinearSolverOptions.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..b40c5fa92f3af73015afa133eaae99b91feb6fda
--- /dev/null
+++ b/src/algebra/LinearSolverOptions.cpp
@@ -0,0 +1,15 @@
+#include <algebra/LinearSolverOptions.hpp>
+
+#include <rang.hpp>
+
+std::ostream&
+operator<<(std::ostream& os, const LinearSolverOptions& options)
+{
+  os << "  library: " << rang::style::bold << name(options.library()) << rang::style::reset << '\n';
+  os << "  method : " << rang::style::bold << name(options.method()) << rang::style::reset << '\n';
+  os << "  precond: " << rang::style::bold << name(options.precond()) << rang::style::reset << '\n';
+  os << "  epsilon: " << rang::style::bold << options.epsilon() << rang::style::reset << '\n';
+  os << "  maxiter: " << rang::style::bold << options.maximumIteration() << rang::style::reset << '\n';
+  os << "  verbose: " << rang::style::bold << std::boolalpha << options.verbose() << rang::style::reset << '\n';
+  return os;
+}
diff --git a/src/algebra/LinearSolverOptions.hpp b/src/algebra/LinearSolverOptions.hpp
new file mode 100644
index 0000000000000000000000000000000000000000..bd7538b53df8740ee6c151e0d2e72a106fdc3c8c
--- /dev/null
+++ b/src/algebra/LinearSolverOptions.hpp
@@ -0,0 +1,233 @@
+#ifndef LINEAR_SOLVER_OPTIONS_HPP
+#define LINEAR_SOLVER_OPTIONS_HPP
+
+#include <utils/Exceptions.hpp>
+
+#include <iostream>
+
+enum class LSLibrary : int8_t
+{
+  LS__begin = 0,
+  //
+  builtin = LS__begin,
+  petsc,
+  //
+  LS__end
+};
+
+enum class LSMethod : int8_t
+{
+  LS__begin = 0,
+  //
+  cg = LS__begin,
+  bicgstab,
+  bicgstab2,
+  gmres,
+  lu,
+  choleski,
+  //
+  LS__end
+};
+
+enum class LSPrecond : int8_t
+{
+  LS__begin = 0,
+  //
+  none = LS__begin,
+  diagonal,
+  incomplete_choleski,
+  incomplete_LU,
+  //
+  LS__end
+};
+
+inline std::string
+name(const LSLibrary library)
+{
+  switch (library) {
+  case LSLibrary::builtin: {
+    return "builtin";
+  }
+  case LSLibrary::petsc: {
+    return "PETSc";
+  }
+  case LSLibrary::LS__end: {
+  }
+  }
+  throw UnexpectedError("Linear system library name is not defined!");
+}
+
+inline std::string
+name(const LSMethod method)
+{
+  switch (method) {
+  case LSMethod::cg: {
+    return "CG";
+  }
+  case LSMethod::bicgstab: {
+    return "BICGStab";
+  }
+  case LSMethod::bicgstab2: {
+    return "BICGStab2";
+  }
+  case LSMethod::gmres: {
+    return "GMRES";
+  }
+  case LSMethod::lu: {
+    return "LU";
+  }
+  case LSMethod::choleski: {
+    return "Choleski";
+  }
+  case LSMethod::LS__end: {
+  }
+  }
+  throw UnexpectedError("Linear system method name is not defined!");
+}
+
+inline std::string
+name(const LSPrecond precond)
+{
+  switch (precond) {
+  case LSPrecond::none: {
+    return "none";
+  }
+  case LSPrecond::diagonal: {
+    return "diagonal";
+  }
+  case LSPrecond::incomplete_choleski: {
+    return "ICholeski";
+  }
+  case LSPrecond::incomplete_LU: {
+    return "ILU";
+  }
+  case LSPrecond::LS__end: {
+  }
+  }
+  throw UnexpectedError("Linear system preconditioner name is not defined!");
+}
+
+template <typename LSEnumType>
+inline LSEnumType
+getLSEnumFromName(const std::string& enum_name)
+{
+  using BaseT = std::underlying_type_t<LSEnumType>;
+  for (BaseT enum_value = static_cast<BaseT>(LSEnumType::LS__begin);
+       enum_value < static_cast<BaseT>(LSEnumType::LS__end); ++enum_value) {
+    if (name(LSEnumType{enum_value}) == enum_name) {
+      return LSEnumType{enum_value};
+    }
+  }
+  throw NormalError(std::string{"could not find '"} + enum_name + "' associate type!");
+}
+
+template <typename LSEnumType>
+inline void
+printLSEnumListNames(std::ostream& os)
+{
+  using BaseT = std::underlying_type_t<LSEnumType>;
+  for (BaseT enum_value = static_cast<BaseT>(LSEnumType::LS__begin);
+       enum_value < static_cast<BaseT>(LSEnumType::LS__end); ++enum_value) {
+    os << "  - " << name(LSEnumType{enum_value}) << '\n';
+  }
+}
+
+class LinearSolverOptions
+{
+ private:
+  LSLibrary m_library = LSLibrary::builtin;
+  LSMethod m_method   = LSMethod::bicgstab;
+  LSPrecond m_precond = LSPrecond::none;
+
+  double m_epsilon           = 1E-6;
+  size_t m_maximum_iteration = 200;
+
+  bool m_verbose = false;
+
+ public:
+  static LinearSolverOptions default_options;
+
+  friend std::ostream& operator<<(std::ostream& os, const LinearSolverOptions& options);
+
+  LSLibrary&
+  library()
+  {
+    return m_library;
+  }
+
+  LSLibrary
+  library() const
+  {
+    return m_library;
+  }
+
+  LSMethod
+  method() const
+  {
+    return m_method;
+  }
+
+  LSMethod&
+  method()
+  {
+    return m_method;
+  }
+
+  LSPrecond
+  precond() const
+  {
+    return m_precond;
+  }
+
+  LSPrecond&
+  precond()
+  {
+    return m_precond;
+  }
+
+  double
+  epsilon() const
+  {
+    return m_epsilon;
+  }
+
+  double&
+  epsilon()
+  {
+    return m_epsilon;
+  }
+
+  size_t&
+  maximumIteration()
+  {
+    return m_maximum_iteration;
+  }
+
+  size_t
+  maximumIteration() const
+  {
+    return m_maximum_iteration;
+  }
+
+  bool&
+  verbose()
+  {
+    return m_verbose;
+  };
+
+  bool
+  verbose() const
+  {
+    return m_verbose;
+  };
+
+  LinearSolverOptions(const LinearSolverOptions&) = default;
+  LinearSolverOptions(LinearSolverOptions&&)      = default;
+
+  LinearSolverOptions()  = default;
+  ~LinearSolverOptions() = default;
+};
+
+inline LinearSolverOptions LinearSolverOptions::default_options;
+
+#endif   // LINEAR_SOLVER_OPTIONS_HPP
diff --git a/src/algebra/LinearSystemSolver.cpp b/src/algebra/LinearSystemSolver.cpp
deleted file mode 100644
index 488d6763d1838cc4d5edc596589310dc2ef66038..0000000000000000000000000000000000000000
--- a/src/algebra/LinearSystemSolver.cpp
+++ /dev/null
@@ -1,331 +0,0 @@
-#include <algebra/LinearSystemSolver.hpp>
-#include <utils/pugs_config.hpp>
-
-#ifdef PUGS_HAS_PETSC
-#include <petsc.h>
-#endif   // PUGS_HAS_PETSC
-
-struct LinearSystemSolver::Internals
-{
-  static bool
-  hasLibrary(LSLibrary library)
-  {
-    switch (library) {
-    case LSLibrary::builtin: {
-      return true;
-    }
-    case LSLibrary::petsc: {
-#ifdef PUGS_HAS_PETSC
-      return true;
-#else
-      return false;
-#endif
-    }
-    default: {
-      throw UnexpectedError("Linear system library (" + name(library) + ") was not set!");
-    }
-    }
-  }
-
-  static void
-  checkHasLibrary(LSLibrary library)
-  {
-    if (not hasLibrary(library)) {
-      throw NormalError(name(library) + " is not linked to pugs. Cannot use it!");
-    }
-  }
-
-  static std::string
-  name(LSLibrary library)
-  {
-    switch (library) {
-    case LSLibrary::builtin: {
-      return "builtin";
-    }
-    case LSLibrary::petsc: {
-      return "PETSc";
-    }
-    default: {
-      throw UnexpectedError("Linear system library name is not defined!");
-    }
-    }
-  }
-
-  static std::string
-  name(LSMethod method)
-  {
-    switch (method) {
-    case LSMethod::cg: {
-      return "conjugate gradient";
-    }
-    case LSMethod::bicgstab: {
-      return "bicg-stab";
-    }
-    case LSMethod::gmres: {
-      return "gmres";
-    }
-    default: {
-      throw UnexpectedError("Linear system method name is not defined!");
-    }
-    }
-  }
-
-  static std::string
-  name(LSPrecond precond)
-  {
-    switch (precond) {
-    case LSPrecond::none: {
-      return "none";
-    }
-    case LSPrecond::diagonal: {
-      return "Jacobi (diagonal)";
-    }
-    case LSPrecond::incomplete_choleski: {
-      return "incomplete Choleski";
-    }
-    case LSPrecond::incomplete_LU: {
-      return "incomplete LU";
-    }
-    default: {
-      throw UnexpectedError("Linear system preconditioner name is not defined!");
-    }
-    }
-  }
-
-  static void
-  checkBuiltinMethod(LSMethod method)
-  {
-    switch (method) {
-    case LSMethod::cg:
-    case LSMethod::bicgstab: {
-      break;
-    }
-    default: {
-      throw NormalError(name(method) + " is not a builtin linear solver!");
-    }
-    }
-  }
-
-  static void
-  checkPETScMethod(LSMethod method)
-  {
-    switch (method) {
-    case LSMethod::cg:
-    case LSMethod::bicgstab:
-    case LSMethod::gmres: {
-      break;
-    }
-    default: {
-      throw NormalError(name(method) + " is not a builtin linear solver!");
-    }
-    }
-  }
-
-  static void
-  checkBuiltinPrecond(LSPrecond precond)
-  {
-    switch (precond) {
-    case LSPrecond::none: {
-      break;
-    }
-    default: {
-      throw NormalError(name(precond) + " is not a builtin preconditioner!");
-    }
-    }
-  }
-
-  static void
-  checkPETScPrecond(LSPrecond precond)
-  {
-    switch (precond) {
-    case LSPrecond::none:
-    case LSPrecond::diagonal:
-    case LSPrecond::incomplete_choleski:
-    case LSPrecond::incomplete_LU: {
-      break;
-    }
-    default: {
-      throw NormalError(name(precond) + " is not a PETSc preconditioner!");
-    }
-    }
-  }
-
-  static void
-  checkOptions(LSLibrary library, LSMethod method, LSPrecond precond)
-  {
-    switch (library) {
-    case LSLibrary::builtin: {
-      checkBuiltinMethod(method);
-      checkBuiltinPrecond(precond);
-      break;
-    }
-    case LSLibrary::petsc: {
-      checkPETScMethod(method);
-      checkPETScPrecond(precond);
-      break;
-    }
-    default: {
-      throw UnexpectedError("Undefined options compatibility for this library (" + name(library) + ")!");
-    }
-    }
-  }
-
-#ifdef PUGS_HAS_PETSC
-
-  static int
-  petscMonitor(KSP, int it, double norm, void*)
-  {
-    std::cout << "iteration: " << it << " residual norm = " << norm << '\n';
-    return 0;
-  }
-
-  static void
-  petscSolveLocalSystem(const SparseMatrixDescriptor<double, size_t>& A,
-                        Vector<double>& x,
-                        const Vector<double>& b,
-                        LSMethod method,
-                        LSPrecond precond,
-                        double epsilon,
-                        size_t maximum_iteration)
-  {
-    Assert(x.size() == b.size() and x.size() == A.numberOfRows());
-
-    Vec petscB;
-    VecCreateMPIWithArray(PETSC_COMM_WORLD, 1, b.size(), b.size(), &b[0], &petscB);
-    Vec petscX;
-    VecCreateMPIWithArray(PETSC_COMM_WORLD, 1, x.size(), x.size(), &x[0], &petscX);
-
-    Mat petscMat;
-    MatCreate(PETSC_COMM_WORLD, &petscMat);
-    MatSetSizes(petscMat, PETSC_DECIDE, PETSC_DECIDE, x.size(), x.size());
-
-    MatSetType(petscMat, MATAIJ);
-    MatSetUp(petscMat);
-
-    for (size_t i = 0; i < A.numberOfRows(); ++i) {
-      const auto& row = A.row(i);
-      PetscInt I      = i;
-      for (auto [j, value] : row.columnIdToValueMap()) {
-        PetscInt J = j;
-        MatSetValues(petscMat, 1, &I, 1, &J, &value, INSERT_VALUES);
-      }
-    }
-
-    MatAssemblyBegin(petscMat, MAT_FINAL_ASSEMBLY);
-    MatAssemblyEnd(petscMat, MAT_FINAL_ASSEMBLY);
-
-    PetscPrintf(PETSC_COMM_WORLD, "Matrix _before_ MatScaleUserImpl() operation\n");
-    MatView(petscMat, PETSC_VIEWER_STDOUT_SELF);
-
-    KSP ksp;
-
-    KSPCreate(PETSC_COMM_WORLD, &ksp);
-    KSPSetTolerances(ksp, epsilon, 1E-100, 1E5, maximum_iteration);
-
-    KSPSetOperators(ksp, petscMat, petscMat);
-
-    switch (method) {
-    case LSMethod::bicgstab: {
-      KSPSetType(ksp, KSPBCGS);
-      break;
-    }
-    case LSMethod::cg: {
-      KSPSetType(ksp, KSPCG);
-      break;
-    }
-    case LSMethod::gmres: {
-      KSPSetType(ksp, KSPGMRES);
-      break;
-    }
-    default: {
-      throw UnexpectedError("unexpected method: " + name(method));
-    }
-    }
-
-    PC pc;
-    KSPGetPC(ksp, &pc);
-
-    switch (precond) {
-    case LSPrecond::diagonal: {
-      PCSetType(pc, PCJACOBI);
-      break;
-    }
-    case LSPrecond::incomplete_LU: {
-      PCSetType(pc, PCILU);
-      break;
-    }
-    case LSPrecond::incomplete_choleski: {
-      PCSetType(pc, PCICC);
-      break;
-    }
-    case LSPrecond::none: {
-      PCSetType(pc, PCNONE);
-      break;
-    }
-    default: {
-      throw UnexpectedError("unexpected preconditioner: " + name(precond));
-    }
-    }
-
-    KSPMonitorSet(ksp, petscMonitor, 0, 0);
-
-    KSPSolve(ksp, petscB, petscX);
-
-    VecView(petscX, PETSC_VIEWER_STDOUT_SELF);
-
-    MatDestroy(&petscMat);
-  }
-
-#else
-
-  static void
-  petscSolveLocalSystem(const SparseMatrixDescriptor<double, size_t>&,
-                        Vector<double>&,
-                        const Vector<double>&,
-                        LSMethod,
-                        LSPrecond,
-                        double,
-                        size_t)
-  {
-    checkHasLibrary(LSLibrary::petsc);
-  }
-
-#endif   // PUGS_HAS_PETSC
-};
-
-bool
-LinearSystemSolver::hasLibrary(LSLibrary library) const
-{
-  return Internals::hasLibrary(library);
-}
-
-LinearSystemSolver::LinearSystemSolver(LSLibrary library,
-                                       LSMethod method,
-                                       LSPrecond precond,
-                                       double epsilon,
-                                       size_t maximum_iteration)
-  : m_library{library}, m_method{method}, m_precond{precond}, m_epsilon{epsilon}, m_maximum_iteration{maximum_iteration}
-{
-  Internals::checkHasLibrary(library);
-  Internals::checkOptions(library, method, precond);
-}
-
-void
-LinearSystemSolver::solveLocalSystem(const SparseMatrixDescriptor<double, size_t>& A,
-                                     Vector<double>& x,
-                                     const Vector<double>& b)
-{
-  switch (m_library) {
-  case LSLibrary::builtin: {
-    throw NotImplementedError("builtin solvers are not plugged yet!");
-    break;
-  }
-  case LSLibrary::petsc: {
-    Internals::petscSolveLocalSystem(A, x, b, m_method, m_precond, m_epsilon, m_maximum_iteration);
-    break;
-  }
-  default: {
-    throw UnexpectedError(Internals::name(m_library) + " cannot solve local systems for sparse matrices");
-  }
-  }
-}
diff --git a/src/algebra/LinearSystemSolver.hpp b/src/algebra/LinearSystemSolver.hpp
deleted file mode 100644
index f689f96ddba12ca8f7f4e4c19bbd78621dd1981f..0000000000000000000000000000000000000000
--- a/src/algebra/LinearSystemSolver.hpp
+++ /dev/null
@@ -1,79 +0,0 @@
-#ifndef LINEAR_SYSTEM_SOLVER_HPP
-#define LINEAR_SYSTEM_SOLVER_HPP
-
-#include <algebra/SparseMatrixDescriptor.hpp>
-#include <algebra/TinyMatrix.hpp>
-#include <algebra/TinyVector.hpp>
-#include <algebra/Vector.hpp>
-
-#include <utils/Exceptions.hpp>
-
-enum class LSLibrary
-{
-  builtin,
-  petsc
-};
-
-enum class LSMethod
-{
-  cg,
-  bicgstab,
-  gmres
-};
-
-enum class LSPrecond
-{
-  none,
-  diagonal,
-  incomplete_choleski,
-  incomplete_LU
-};
-
-class LinearSystemSolver
-{
- private:
-  struct Internals;
-
-  const LSLibrary m_library;
-  const LSMethod m_method;
-  const LSPrecond m_precond;
-
-  const double m_epsilon;
-  const size_t m_maximum_iteration;
-
-  bool m_is_verbose = false;
-
-  void _solveLocalDense(size_t N, const double* A, double* x, const double* b);
-
- public:
-  bool
-  isVerbose() const
-  {
-    return m_is_verbose;
-  }
-
-  void
-  setVerbose(bool verbose)
-  {
-    m_is_verbose = verbose;
-  }
-
-  bool hasLibrary(LSLibrary library) const;
-
-  void solveLocalSystem(const SparseMatrixDescriptor<double, size_t>& A, Vector<double>& x, const Vector<double>& b);
-
-  template <size_t N>
-  void
-  solveLocalSystem(const TinyMatrix<N>& A, TinyVector<N>& x, const TinyVector<N>& b)
-  {
-    this->_solveLocalDense(N, &A(0, 0), &x[0], &b[0]);
-  }
-
-  LinearSystemSolver(LSLibrary library,
-                     LSMethod method,
-                     LSPrecond precond,
-                     double epsilon           = 1e-6,
-                     size_t maximum_iteration = 100);
-};
-
-#endif   // LINEAR_SYSTEM_SOLVER_HPP
diff --git a/src/algebra/PETScWrapper.cpp b/src/algebra/PETScWrapper.cpp
index 76e56692a67e86bb61f6333c09680a30bc9e07ae..dd11dc9772f11ad29ca4970c5b88656c623a3508 100644
--- a/src/algebra/PETScWrapper.cpp
+++ b/src/algebra/PETScWrapper.cpp
@@ -12,6 +12,7 @@ void
 initialize([[maybe_unused]] int& argc, [[maybe_unused]] char* argv[])
 {
 #ifdef PUGS_HAS_PETSC
+  PetscOptionsSetValue(NULL, "-no_signal_handler", "true");
   PetscInitialize(&argc, &argv, 0, 0);
 #endif   // PUGS_HAS_PETSC
 }
diff --git a/src/algebra/SparseMatrixDescriptor.hpp b/src/algebra/SparseMatrixDescriptor.hpp
index 09f13085b4881d2d602d41a42e0d8d0918cca633..d5c14713bb6b91235b796a56f40b9a2f5a605805 100644
--- a/src/algebra/SparseMatrixDescriptor.hpp
+++ b/src/algebra/SparseMatrixDescriptor.hpp
@@ -151,7 +151,12 @@ class SparseMatrixDescriptor
     return values;
   }
 
-  SparseMatrixDescriptor(size_t nb_row) : m_row_array{nb_row} {}
+  SparseMatrixDescriptor(size_t nb_row) : m_row_array{nb_row}
+  {
+    for (size_t i = 0; i < nb_row; ++i) {
+      m_row_array[i][i] = 0;
+    }
+  }
 
   ~SparseMatrixDescriptor() = default;
 };
diff --git a/src/language/ast/ASTNodeDataType.cpp b/src/language/ast/ASTNodeDataType.cpp
index 10ec58b451ead8402a328744cb977c29557dbbbf..ce2bbcc60182e0fe025d4836ee43fe0cb6d37a59 100644
--- a/src/language/ast/ASTNodeDataType.cpp
+++ b/src/language/ast/ASTNodeDataType.cpp
@@ -48,11 +48,15 @@ dataTypeName(const ASTNodeDataType& data_type)
   case ASTNodeDataType::list_t: {
     std::ostringstream data_type_name_list;
     const auto& data_type_list = data_type.contentTypeList();
-    data_type_name_list << dataTypeName(*data_type_list[0]);
-    for (size_t i = 1; i < data_type_list.size(); ++i) {
-      data_type_name_list << '*' << dataTypeName(*data_type_list[i]);
+    if (data_type_list.size() > 0) {
+      data_type_name_list << dataTypeName(*data_type_list[0]);
+      for (size_t i = 1; i < data_type_list.size(); ++i) {
+        data_type_name_list << '*' << dataTypeName(*data_type_list[i]);
+      }
+      name = "list(" + data_type_name_list.str() + ")";
+    } else {
+      name = "list(void)";
     }
-    name = "list(" + data_type_name_list.str() + ")";
     break;
   }
   case ASTNodeDataType::string_t:
diff --git a/src/language/modules/CMakeLists.txt b/src/language/modules/CMakeLists.txt
index f8cf2f0b445882a672d54e60dbc75858bbb246c7..0a996fd6764b4d2eed57c02e8682283f1e640901 100644
--- a/src/language/modules/CMakeLists.txt
+++ b/src/language/modules/CMakeLists.txt
@@ -2,6 +2,7 @@
 
 add_library(PugsLanguageModules
   BuiltinModule.cpp
+  LinearSolverModule.cpp
   MathModule.cpp
   MeshModule.cpp
   ModuleRepository.cpp
diff --git a/src/language/modules/LinearSolverModule.cpp b/src/language/modules/LinearSolverModule.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..9e626ba2b0e4707df0495de2057a00d81ea4b118
--- /dev/null
+++ b/src/language/modules/LinearSolverModule.cpp
@@ -0,0 +1,85 @@
+#include <language/modules/LinearSolverModule.hpp>
+
+#include <algebra/LinearSolver.hpp>
+#include <language/utils/BuiltinFunctionEmbedder.hpp>
+#include <language/utils/TypeDescriptor.hpp>
+
+LinearSolverModule::LinearSolverModule()
+{
+  this->_addBuiltinFunction("setLSVerbosity", std::make_shared<BuiltinFunctionEmbedder<void(const bool&)>>(
+
+                                                [](const bool& verbose) -> void {
+                                                  LinearSolverOptions::default_options.verbose() = verbose;
+                                                }
+
+                                                ));
+
+  this->_addBuiltinFunction("setLSEpsilon", std::make_shared<BuiltinFunctionEmbedder<void(const double&)>>(
+
+                                              [](const double& epsilon) -> void {
+                                                LinearSolverOptions::default_options.epsilon() = epsilon;
+                                              }
+
+                                              ));
+
+  this->_addBuiltinFunction("setLSMaxIter", std::make_shared<BuiltinFunctionEmbedder<void(const uint64_t&)>>(
+
+                                              [](const uint64_t& max_iter) -> void {
+                                                LinearSolverOptions::default_options.maximumIteration() = max_iter;
+                                              }
+
+                                              ));
+
+  this->_addBuiltinFunction("setLSLibrary", std::make_shared<BuiltinFunctionEmbedder<void(const std::string&)>>(
+
+                                              [](const std::string& library_name) -> void {
+                                                LinearSolverOptions::default_options.library() =
+                                                  getLSEnumFromName<LSLibrary>(library_name);
+                                              }
+
+                                              ));
+
+  this->_addBuiltinFunction("setLSMethod", std::make_shared<BuiltinFunctionEmbedder<void(const std::string&)>>(
+
+                                             [](const std::string& method_name) -> void {
+                                               LinearSolverOptions::default_options.method() =
+                                                 getLSEnumFromName<LSMethod>(method_name);
+                                             }
+
+                                             ));
+
+  this->_addBuiltinFunction("setLSPrecond", std::make_shared<BuiltinFunctionEmbedder<void(const std::string&)>>(
+
+                                              [](const std::string& precond_name) -> void {
+                                                LinearSolverOptions::default_options.precond() =
+                                                  getLSEnumFromName<LSPrecond>(precond_name);
+                                              }
+
+                                              ));
+
+  this->_addBuiltinFunction("printLSOptions", std::make_shared<BuiltinFunctionEmbedder<void()>>(
+
+                                                []() -> void {
+                                                  std::cout << rang::fgB::yellow << "Linear solver options"
+                                                            << rang::style::reset << '\n';
+                                                  std::cout << LinearSolverOptions::default_options;
+                                                }
+
+                                                ));
+
+  this->_addBuiltinFunction("printLSAvailable",
+                            std::make_shared<BuiltinFunctionEmbedder<void()>>(
+
+                              []() -> void {
+                                std::cout << rang::fgB::yellow << "Available linear solver options"
+                                          << rang::style::reset << '\n';
+                                std::cout << rang::fgB::blue << " libraries" << rang::style::reset << '\n';
+                                printLSEnumListNames<LSLibrary>(std::cout);
+                                std::cout << rang::fgB::blue << " methods" << rang::style::reset << '\n';
+                                printLSEnumListNames<LSMethod>(std::cout);
+                                std::cout << rang::fgB::blue << " preconditioners" << rang::style::reset << '\n';
+                                printLSEnumListNames<LSPrecond>(std::cout);
+                              }
+
+                              ));
+}
diff --git a/src/language/modules/LinearSolverModule.hpp b/src/language/modules/LinearSolverModule.hpp
new file mode 100644
index 0000000000000000000000000000000000000000..5dc7ae64efd3ed43f554e821693f761b0a66d412
--- /dev/null
+++ b/src/language/modules/LinearSolverModule.hpp
@@ -0,0 +1,19 @@
+#ifndef LINEAR_SOLVER_MODULE_HPP
+#define LINEAR_SOLVER_MODULE_HPP
+
+#include <language/modules/BuiltinModule.hpp>
+
+class LinearSolverModule : public BuiltinModule
+{
+ public:
+  std::string_view
+  name() const final
+  {
+    return "linear_solver";
+  }
+
+  LinearSolverModule();
+  ~LinearSolverModule() = default;
+};
+
+#endif   // LINEAR_SOLVER_MODULE_HPP
diff --git a/src/language/modules/ModuleRepository.cpp b/src/language/modules/ModuleRepository.cpp
index 497ba083ac2d9d2ca0359c5d73e85e094b1fed0e..df403fa87f0c0d39778414a92ec7aa991b3d8d5b 100644
--- a/src/language/modules/ModuleRepository.cpp
+++ b/src/language/modules/ModuleRepository.cpp
@@ -1,6 +1,7 @@
 #include <language/modules/ModuleRepository.hpp>
 
 #include <language/ast/ASTNode.hpp>
+#include <language/modules/LinearSolverModule.hpp>
 #include <language/modules/MathModule.hpp>
 #include <language/modules/MeshModule.hpp>
 #include <language/modules/SchemeModule.hpp>
@@ -23,6 +24,7 @@ ModuleRepository::ModuleRepository()
   this->_subscribe(std::make_unique<MeshModule>());
   this->_subscribe(std::make_unique<VTKModule>());
   this->_subscribe(std::make_unique<SchemeModule>());
+  this->_subscribe(std::make_unique<LinearSolverModule>());
 }
 
 template <typename NameEmbedderMapT, typename EmbedderTableT>
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index 8b2a7c5516394444debece5e32413dde7804c56d..8d0344a03785fc30e30a20b71b498d7cd2b28d4a 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -47,7 +47,7 @@ add_executable (unit_tests
   test_BuiltinFunctionEmbedder.cpp
   test_BuiltinFunctionEmbedderTable.cpp
   test_BuiltinFunctionProcessor.cpp
-  test_MathModule.cpp
+  test_CG.cpp
   test_ContinueProcessor.cpp
   test_ConcatExpressionProcessor.cpp
   test_CRSMatrix.cpp
@@ -65,9 +65,9 @@ add_executable (unit_tests
   test_INodeProcessor.cpp
   test_ItemType.cpp
   test_ListAffectationProcessor.cpp
+  test_MathModule.cpp
   test_NameProcessor.cpp
   test_OStreamProcessor.cpp
-  test_PCG.cpp
   test_PugsFunctionAdapter.cpp
   test_PugsAssert.cpp
   test_RevisionInfo.cpp
@@ -98,6 +98,7 @@ target_link_libraries (unit_tests
   kokkos
   ${PARMETIS_LIBRARIES}
   ${MPI_CXX_LINK_FLAGS} ${MPI_CXX_LIBRARIES}
+  ${PETSC_LIBRARIES}
   Catch2
   )
 
@@ -108,6 +109,7 @@ target_link_libraries (mpi_unit_tests
   kokkos
   ${PARMETIS_LIBRARIES}
   ${MPI_CXX_LINK_FLAGS} ${MPI_CXX_LIBRARIES}
+  ${PETSC_LIBRARIES}
   Catch2
   )
 
diff --git a/tests/test_BiCGStab.cpp b/tests/test_BiCGStab.cpp
index 99b94515ba7795903434db761d509b9052fcaf71..49a6955be4ae1da7c45e036977a3036be0ccf6d3 100644
--- a/tests/test_BiCGStab.cpp
+++ b/tests/test_BiCGStab.cpp
@@ -45,7 +45,7 @@ TEST_CASE("BiCGStab", "[algebra]")
     Vector<double> x{5};
     x = 0;
 
-    BiCGStab<false>{b, A, x, 10, 1e-12};
+    BiCGStab{A, x, b, 1e-12, 10, false};
     Vector error = x - x_exact;
     REQUIRE(std::sqrt((error, error)) < 1E-10 * std::sqrt((x, x)));
   }
@@ -88,7 +88,7 @@ TEST_CASE("BiCGStab", "[algebra]")
     Vector<double> x{5};
     x = 0;
 
-    BiCGStab{b, A, x, 1, 1e-12};
+    BiCGStab{A, x, b, 1e-12, 1, true};
     Vector error = x - x_exact;
     REQUIRE(std::sqrt((error, error)) > 1E-5 * std::sqrt((x, x)));
   }
diff --git a/tests/test_PCG.cpp b/tests/test_CG.cpp
similarity index 91%
rename from tests/test_PCG.cpp
rename to tests/test_CG.cpp
index d4564761d8c564082e4668360e5a2e2a8ecce008..2ce9febb0a31b087d2a7651e4442245b9d6c51ce 100644
--- a/tests/test_PCG.cpp
+++ b/tests/test_CG.cpp
@@ -1,11 +1,11 @@
 #include <catch2/catch.hpp>
 
+#include <algebra/CG.hpp>
 #include <algebra/CRSMatrix.hpp>
-#include <algebra/PCG.hpp>
 
 // clazy:excludeall=non-pod-global-static
 
-TEST_CASE("PCG", "[algebra]")
+TEST_CASE("CG", "[algebra]")
 {
   SECTION("no preconditionner")
   {
@@ -45,7 +45,7 @@ TEST_CASE("PCG", "[algebra]")
     Vector<double> x{5};
     x = 0;
 
-    PCG{b, A, A, x, 10, 1e-12};
+    CG{A, x, b, 1e-12, 10};
     Vector error = x - x_exact;
     REQUIRE(std::sqrt((error, error)) < 1E-10 * std::sqrt((x, x)));
   }
@@ -62,7 +62,7 @@ TEST_CASE("PCG", "[algebra]")
     Vector<double> x{5};
     x = 0;
 
-    PCG<false>{b, A, A, x, 10, 1e-12};
+    CG{A, x, b, 1e-12, 10, false};
     REQUIRE(std::sqrt((x, x)) == 0);
   }
 
@@ -104,7 +104,7 @@ TEST_CASE("PCG", "[algebra]")
     Vector<double> x{5};
     x = 0;
 
-    PCG<false>{b, A, A, x, 1, 1e-12};
+    CG{A, x, b, 1e-12, 1, false};
     Vector error = x - x_exact;
     REQUIRE(std::sqrt((error, error)) > 1E-10 * std::sqrt((x, x)));
   }
diff --git a/tests/test_SparseMatrixDescriptor.cpp b/tests/test_SparseMatrixDescriptor.cpp
index cd66380b1d1beb6bcb9ba1a9c0d9c495947a3235..f90cc83b3778e39a3319824f53a34e2041dadcf7 100644
--- a/tests/test_SparseMatrixDescriptor.cpp
+++ b/tests/test_SparseMatrixDescriptor.cpp
@@ -68,18 +68,18 @@ TEST_CASE("SparseMatrixDescriptor", "[algebra]")
     S(4, 1) = 1;
     S(4, 4) = -2;
 
-    REQUIRE(S.row(0).numberOfValues() == 1);
+    REQUIRE(S.row(0).numberOfValues() == 2);
     REQUIRE(S.row(1).numberOfValues() == 2);
     REQUIRE(S.row(2).numberOfValues() == 1);
-    REQUIRE(S.row(3).numberOfValues() == 1);
+    REQUIRE(S.row(3).numberOfValues() == 2);
     REQUIRE(S.row(4).numberOfValues() == 2);
 
     const auto& const_S = S;
 
-    REQUIRE(const_S.row(0).numberOfValues() == 1);
+    REQUIRE(const_S.row(0).numberOfValues() == 2);
     REQUIRE(const_S.row(1).numberOfValues() == 2);
     REQUIRE(const_S.row(2).numberOfValues() == 1);
-    REQUIRE(const_S.row(3).numberOfValues() == 1);
+    REQUIRE(const_S.row(3).numberOfValues() == 2);
     REQUIRE(const_S.row(4).numberOfValues() == 2);
 
 #ifndef NDEBUG
@@ -126,7 +126,7 @@ TEST_CASE("SparseMatrixDescriptor", "[algebra]")
     const auto graph = S.graphVector();
 
     REQUIRE(graph.size() == S.numberOfRows());
-    REQUIRE(graph[0].size() == 1);
+    REQUIRE(graph[0].size() == 2);
     REQUIRE(graph[1].size() == 2);
     REQUIRE(graph[2].size() == 1);
     REQUIRE(graph[3].size() == 2);
@@ -157,7 +157,7 @@ TEST_CASE("SparseMatrixDescriptor", "[algebra]")
 
     const auto value_array = S.valueArray();
 
-    REQUIRE(value_array.size() == 8);
+    REQUIRE(value_array.size() == 9);
 
     REQUIRE(value_array[0] == 5);
     REQUIRE(value_array[1] == 1);
@@ -186,7 +186,7 @@ TEST_CASE("SparseMatrixDescriptor", "[algebra]")
     output << '\n' << S;
 
     std::string expected_output = R"(
-0 | 2:5
+0 | 0:0 2:5
 1 | 1:1 2:11
 2 | 2:4
 3 | 1:-3 3:5