test3 Namespace Reference

This test checks that the CG solver converges to u_random for the RHS set as b_c = A_CG * u_random with some vector u_random. More...

Variables
	parser = argparse.ArgumentParser(description='Multigrid - Poisson solver')
	dest
	type
	int
	default
	help
	action
	False
	choices
	required
	True
	args = parser.parse_args()
	project
	poisson_equation_matrices
	system_matrix
	system_matrix_scaling
	mass_matrix
	mass_matrix_scaling
	solver
	build_mode = peano4.api.output.CompileMode.RELEASE
float	cube_size = 1.0
	dimensions
	offset
	domain_size
	plot_after_each_mesh_sweep
	max_iterations
	peano4_project = project.generate_Peano4_project(args.verbose)

Detailed Description

This test checks that the CG solver converges to u_random for the RHS set as b_c = A_CG * u_random with some vector u_random.

It shows that the solution u of the problem A * u = A * u_random approximates u_random. u_random has to satisfy the boundary conditions but can be random at the interior vertices.

Algorithm:

1. Generate u_random by assigning a value from [0,1] to each vertex.
2. Set u_random to 0 at the boundary vertices to satisfy the boundary conditions.
3. Compute b_c = A_CG * u_random, where A_CG is the system matrix for CG.
4. Solve A_CG * u = b_c with CollocatedSolver.
5. Check |u - u_random| < tol.

Variable Documentation

action

test3.action

Definition at line 37 of file test3.py.

args

test3.args = parser.parse_args()

Definition at line 43 of file test3.py.

build_mode

test3.build_mode = peano4.api.output.CompileMode.RELEASE

Definition at line 88 of file test3.py.

choices

test3.choices

Definition at line 42 of file test3.py.

cube_size

float test3.cube_size = 1.0

Definition at line 96 of file test3.py.

default

test3.default

Definition at line 36 of file test3.py.

dest

test3.dest

Definition at line 36 of file test3.py.

dimensions

test3.dimensions

Definition at line 98 of file test3.py.

domain_size

test3.domain_size

Definition at line 100 of file test3.py.

False

test3.False

Definition at line 37 of file test3.py.

help

test3.help

Definition at line 36 of file test3.py.

int

test3.int

Definition at line 36 of file test3.py.

mass_matrix

test3.mass_matrix

Definition at line 62 of file test3.py.

mass_matrix_scaling

test3.mass_matrix_scaling

Definition at line 62 of file test3.py.

max_iterations

test3.max_iterations

Definition at line 102 of file test3.py.

offset

test3.offset

Definition at line 99 of file test3.py.

parser

test3.parser = argparse.ArgumentParser(description='Multigrid - Poisson solver')

Definition at line 35 of file test3.py.

peano4_project

test3.peano4_project = project.generate_Peano4_project(args.verbose)

Definition at line 108 of file test3.py.

plot_after_each_mesh_sweep

test3.plot_after_each_mesh_sweep

Definition at line 101 of file test3.py.

poisson_equation_matrices

test3.poisson_equation_matrices

Initial value:

=  mghype.api.matrixgenerators.DLinearMassIdentity(
  dimensions = args.dimensions,
  poly_degree = 1,
  unknowns_per_node = 1
)

Definition at line 55 of file test3.py.

project

test3.project

Initial value:

=  mghype.matrixfree.api.Project( project_name = "CollocatedFEM", 
                              namespace = [ "tests", "multigrid", "matrixfree", "verifyRandom" ]
                                )

Definition at line 45 of file test3.py.

required

test3.required

Definition at line 42 of file test3.py.

solver

test3.solver

Initial value:

=  mghype.matrixfree.solvers.api.CollocatedDLinearDiscretisationWithPointJacobi("CollocatedPoisson",
                                                              1, # unknowns
                                                              args.dimensions,
                                                              args.meshsize,
                                                              args.meshsize,
                                                              local_assembly_matrix = system_matrix,
                                                              local_assembly_matrix_scaling=system_matrix_scaling,
                                                              mass_matrix = mass_matrix,
                                                              mass_matrix_scaling = mass_matrix_scaling,
                                                              solver_tolerance=1e-9,
                                                              custom_init_actionset=InitDofsCollocatedRandomRhs,
                                                              custom_plot_actionset=[("rand","getRand")]
                                                            )

Definition at line 65 of file test3.py.

system_matrix

test3.system_matrix

Definition at line 61 of file test3.py.

system_matrix_scaling

test3.system_matrix_scaling

Definition at line 61 of file test3.py.

True

test3.True

Definition at line 42 of file test3.py.

type

test3.type

Definition at line 36 of file test3.py.