petsc-master 2015-10-08
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KSP
solving a system of linear equations
Solves a tridiagonal linear system with KSP.
solving a system of linear equations
Solves a linear system in parallel with KSP.
Input parameters include:
-m <mesh_x> : number of mesh points in x-direction
-n <mesh_n> : number of mesh points in y-direction
solving a system of linear equations
Description: Solves a tridiagonal linear system with KSP.
solving a system of linear equations
Solves 2D inhomogeneous Laplacian using multigrid.
solving a system of linear equations
Solves 2D compressible Euler.
solving a system of linear equations
Solves 2D inhomogeneous Laplacian using multigrid.
solving a system of linear equations
Solves 3D Laplacian using multigrid.
solving a system of linear equations
Description: Solve Ax=b. A comes from an anisotropic 2D thermal problem with Q1 FEM on domain (-1,1)^2.
Material conductivity given by tensor:
D = | 1 0 |
| 0 epsilon |
rotated by angle 'theta' (-theta <90> in degrees) with anisotropic parameter 'epsilon' (-epsilon <0.0>).
Blob right hand side centered at C (-blob_center C(1),C(2) <0,0>)
Dirichlet BCs on y=-1 face.
-out_matlab will generate binary files for A,x,b and a ex54f.m file that reads them and plots them in matlab.
User can change anisotropic shape with function ex54_psi(). Negative theta will switch to a circular anisotropy.
solving a system of linear equations
Solves a tridiagonal linear system with KSP.
basic parallel example;
basic parallel example;
Solves a linear system in parallel with KSP.
Input parameters include:
-random_exact_sol : use a random exact solution vector
-view_exact_sol : write exact solution vector to stdout
-m <mesh_x> : number of mesh points in x-direction
-n <mesh_n> : number of mesh points in y-direction
basic parallel example;
Solves a tridiagonal linear system.
basic parallel example;
Solves a linear system in parallel with KSP and DM.
Compare this to ex2 which solves the same problem without a DM.
Laplacian, 2d
Solves a linear system in parallel with KSP.
Input parameters include:
-m <mesh_x> : number of mesh points in x-direction
-n <mesh_n> : number of mesh points in y-direction
Laplacian, 2d
Solves a variable Poisson problem with KSP.
Laplacian, 2d
Laplacian, 2d
Solves a sequence of linear systems with different right-hand-side vectors.
Input parameters include:
-ntimes <ntimes> : number of linear systems to solve
-view_exact_sol : write exact solution vector to stdout
-m <mesh_x> : number of mesh points in x-direction
-n <mesh_n> : number of mesh points in y-direction
Laplacian, 2d
Laplacian, 2d
Solves a linear system in parallel with KSP.
Input parameters include:
-random_exact_sol : use a random exact solution vector
-view_exact_sol : write exact solution vector to stdout
-m <mesh_x> : number of mesh points in x-direction
-n <mesh_n> : number of mesh points in y-direction
Laplacian, 2d
Solves 2D inhomogeneous Laplacian using multigrid.
Laplacian, 2d
Solves 2D inhomogeneous Laplacian using multigrid.
Laplacian, 2d
Solves a linear system in parallel with KSP and DM.
Compare this to ex2 which solves the same problem without a DM.
basic parallel example
Solves a linear system in parallel with KSP. Also
illustrates setting a user-defined shell preconditioner and using the
macro __FUNCT__ to define routine names for use in error handling.
Input parameters include:
-user_defined_pc : Activate a user-defined preconditioner
basic parallel example
Solves a linear system in parallel with KSP. Also indicates
use of a user-provided preconditioner. Input parameters include:
-user_defined_pc : Activate a user-defined preconditioner
basic parallel example
Solves a linear system in parallel with KSP. Also indicates
use of a user-provided preconditioner. Input parameters include:
basic parallel example
Description: Solves a linear system in parallel with KSP (Fortran code).
Also shows how to set a user-defined monitoring routine.
basic parallel example
Bilinear elements on the unit square for Laplacian. To test the parallel
matrix assembly, the matrix is intentionally laid out across processors
differently from the way it is assembled. Input arguments are:
-m <size> : problem size
repeatedly solving linear systems;
Solves a sequence of linear systems with different right-hand-side vectors.
Input parameters include:
-ntimes <ntimes> : number of linear systems to solve
-view_exact_sol : write exact solution vector to stdout
-m <mesh_x> : number of mesh points in x-direction
-n <mesh_n> : number of mesh points in y-direction
repeatedly solving linear systems;
Solves two linear systems in parallel with KSP. The code
illustrates repeated solution of linear systems with the same preconditioner
method but different matrices (having the same nonzero structure). The code
also uses multiple profiling stages. Input arguments are
-m <size> : problem size
-mat_nonsym : use nonsymmetric matrix (default is symmetric)
repeatedly solving linear systems;
Description: This example demonstrates repeated linear solves as
well as the use of different preconditioner and linear system
matrices. This example also illustrates how to save PETSc objects
in common blocks.
repeatedly solving linear systems;
The solution of 2 different linear systems with different linear solvers.
Also, this example illustrates the repeated
solution of linear systems, while reusing matrix, vector, and solver data
structures throughout the process. Note the various stages of event logging.
customizing the block Jacobi preconditioner
Block Jacobi preconditioner for solving a linear system in parallel with KSP.
The code indicates the
procedures for setting the particular block sizes and for using different
linear solvers on the individual blocks.
Additive Schwarz Method (ASM) with user-defined subdomains
Illustrates use of the preconditioner ASM.
The Additive Schwarz Method for solving a linear system in parallel with KSP. The
code indicates the procedure for setting user-defined subdomains. Input
parameters include:
-user_set_subdomain_solvers: User explicitly sets subdomain solvers
-user_set_subdomains: Activate user-defined subdomains
solving a linear system
Reads a PETSc matrix and vector from a file and solves a linear system.
This version first preloads and solves a small system, then loads
another (larger) system and solves it as well. This example illustrates
preloading of instructions with the smaller system so that more accurate
performance monitoring can be done with the larger one (that actually
is the system of interest). See the 'Performance Hints' chapter of the
users manual for a discussion of preloading. Input parameters include
-f0 <input_file> : first file to load (small system)
-f1 <input_file> : second file to load (larger system)
-nearnulldim <0> : number of vectors in the near-null space immediately following matrix
-trans : solve transpose system instead
solving a linear system
Reads a PETSc matrix and vector from a file and solves the normal equations.
solving a linear system
Reads a PETSc matrix and vector from a socket connection, solves a linear system and sends the result back.
solving a Helmholtz equation
Solves a linear system in parallel with KSP.
solving a Helmholtz equation
Description: Solves a complex linear system in parallel with KSP (Fortran code).
basic sequential example
Solves a variable Poisson problem with KSP.
basic sequential example
semi-implicit
Solves 2D compressible Euler.
Laplacian, 3d
Solves 3D Laplacian using multigrid.
Additive Schwarz Method (GASM) with user-defined subdomains
Illustrates use of the preconditioner GASM.
The Additive Schwarz Method for solving a linear system in parallel with KSP. The
code indicates the procedure for setting user-defined subdomains.
See section 'ex62' below for command-line options.
Without -user_set_subdomains, the general PCGASM options are meaningful:
-pc_gasm_total_subdomains
-pc_gasm_print_subdomains
Additive Schwarz Method (GASM) with user-defined subdomains
Illustrates use of the preconditioner GASM.
using hierarchical partitioning and MatIncreaseOverlapSplit -pc_gasm_total_subdomains
-pc_gasm_print_subdomains
setting a user-defined monitoring routine
Description: Solves a linear system in parallel with KSP (Fortran code).
Also shows how to set a user-defined monitoring routine.
different matrices for linear system and preconditioner;
Description: This example demonstrates repeated linear solves as
well as the use of different preconditioner and linear system
matrices. This example also illustrates how to save PETSc objects
in common blocks.
writing a user-defined nonlinear solver
Solves a nonlinear system in parallel with a user-defined
Newton method that uses KSP to solve the linearized Newton sytems. This solver
is a very simplistic inexact Newton method. The intent of this code is to
demonstrate the repeated solution of linear sytems with the same nonzero pattern.
This is NOT the recommended approach for solving nonlinear problems with PETSc!
We urge users to employ the SNES component for solving nonlinear problems whenever
possible, as it offers many advantages over coding nonlinear solvers independently.
We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
domain, using distributed arrays (DMDAs) to partition the parallel grid.