petsc-master 2014-09-22
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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 using multigrid.
• 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
• 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. Input
parameters include:
-M: Number of mesh points in the x direction
-N: Number of mesh points in the y direction
-user_set_subdomain_solvers: User explicitly sets subdomain solvers
-user_set_subdomains: Use the user-provided subdomain partitioning routine
With -user_set_subdomains on, the following options are meaningful:
-Mdomains: Number of subdomains in the x direction
-Ndomains: Number of subdomains in the y direction
-overlap: Size of domain overlap in terms of the number of mesh lines in x and y
General useful options:
-pc_gasm_print_subdomains: Print the index sets defining the 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 using multigrid.
• Laplacian, 3d Solves 3D Laplacian using multigrid.
• 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.