PETScLinearSolver.solve(A, b, x0=None, solver_type='cg', precondioner='jacobi', maxiter=None, atol=None, rtol=None)[source]

Solves and returns the solution to the linear system, Ax = b.

This method converts the solution vector from a PETSc.Vec instance to a numpy array, and finally destroys all the PETSc objects to free memory.

  • A (csr_matrix) – Coefficients matrix in Ax = b

  • b (ndarray) – Right-hand-side vector in Ax = b

  • solver_type (str, optional) – Default is the iterative solver ‘cg’ based on the Conjugate Gradient method.

  • preconditioner (str, optional) – Default is the ‘jacobi’ preconditioner, i.e., diagonal scaling preconditioning. The preconditioner is used with iterative solvers. When a direct solver is used, this parameter is ignored.

  • factorization_type (str, optional) – The factorization type used with the direct solver. Default is ‘lu’. This parameter is ignored when an iterative solver is used.


The solution to Ax = b

Return type



Certain combinations of iterative solvers and precondioners or direct solvers and factorization types are not supported. The summary table of the different possibilities can be found here