Implementing a User-Defined Preconditioner in PETSc

To implement a user-defined preconditioner in PETSc, you’ll need to create a custom preconditioner class that implements the required operations. Here’s a step-by-step guide:

Basic Approach

1. Create a context structure to hold your preconditioner data
2. Implement required operations (setup and apply)
3. Register your preconditioner with PETSc
4. Use your preconditioner in your solver

Example Implementation

Here’s a basic template for a user-defined preconditioner:

#include <petscpc.h>typedef struct {Mat local_matrix;  // Example field - customize for your needsVec work_vector;   // Example field - customize for your needs
} MyPC;static PetscErrorCode MyPCSetUp(PC pc)
{MyPC *mypc;Mat A;PetscFunctionBegin;PetscCall(PCGetOperators(pc, &A, NULL));PetscCall(PCGetApplicationContext(pc, (void**)&mypc));// Setup your preconditioner here// For example, extract diagonal or create approximate inversePetscFunctionReturn(0);
}static PetscErrorCode MyPCApply(PC pc, Vec x, Vec y)
{MyPC *mypc;PetscFunctionBegin;PetscCall(PCGetApplicationContext(pc, (void**)&mypc));// Apply your preconditioner here: y = M?1 x// For a simple example, Jacobi preconditioner:PetscCall(VecPointwiseDivide(y, x, mypc->diagonal));PetscFunctionReturn(0);
}static PetscErrorCode MyPCDestroy(PC pc)
{MyPC *mypc;PetscFunctionBegin;PetscCall(PCGetApplicationContext(pc, (void**)&mypc));// Clean up your dataif (mypc) {if (mypc->local_matrix) PetscCall(MatDestroy(&mypc->local_matrix));if (mypc->work_vector) PetscCall(VecDestroy(&mypc->work_vector));PetscCall(PetscFree(mypc));}PetscFunctionReturn(0);
}PetscErrorCode PCCreate_MyPC(PC pc)
{MyPC *mypc;PetscFunctionBegin;PetscCall(PetscNew(&mypc));PetscCall(PCSetApplicationContext(pc, (void*)mypc));// Set function pointersPetscCall(PCSetSetUp(pc, MyPCSetUp));PetscCall(PCSetApply(pc, MyPCApply));PetscCall(PCSetDestroy(pc, MyPCDestroy));PetscFunctionReturn(0);
}

Using Your Preconditioner

1. First register your preconditioner:

PetscErrorCode RegisterMyPC()
{PetscFunctionBegin;PetscCall(PCRegister("mypc", PCCreate_MyPC));PetscFunctionReturn(0);
}

2. Then use it in your code:

PC pc;
KSP ksp;// Create KSP solver
PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
PetscCall(KSPSetType(ksp, KSPGMRES));// Get the preconditioner context
PetscCall(KSPGetPC(ksp, &pc));// Set your preconditioner
PetscCall(PCSetType(pc, "mypc"));// Set up and solve
PetscCall(KSPSetUp(ksp));
PetscCall(KSPSolve(ksp, b, x));

Advanced Options

For more complex preconditioners, you might also want to implement:

• PCSetFromOptions - to configure your PC from command line options
• PCView - to display information about your preconditioner
• Additional operations like PCApplyTranspose if needed

Important Notes

1. PETSc provides several built-in preconditioners - consider if one of those meets your needs before implementing your own.
2. For parallel implementations, you’ll need to handle data distribution carefully.
3. Profile your preconditioner to ensure it’s actually improving performance.

Would you like me to elaborate on any specific aspect of implementing a user-defined preconditioner in PETSc?

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Using PCShell to Implement User-Defined Preconditioners in PETSc

PCShell is a flexible way to implement your own custom preconditioners in PETSc. Here’s how to use it:

Basic Implementation Steps

1. Create the PCShell context:

   typedef struct {/* Your preconditioner data goes here */Mat A;              // matrix being preconditionedVec work1, work2;   // work vectors/* Add any other data your preconditioner needs */
   } MyPC;
   

2. Implement the setup function:

   static PetscErrorCode MyPCSetup(PC pc)
   {MyPC *mypc;PCShellGetContext(pc, (void**)&mypc);Mat A;PCGetOperators(pc, &A, NULL);mypc->A = A;// Create work vectorsMatCreateVecs(A, &mypc->work1, &mypc->work2);/* Any other setup your preconditioner needs */return 0;
   }
   

3. Implement the apply function:

   static PetscErrorCode MyPCApply(PC pc, Vec x, Vec y)
   {MyPC *mypc;PCShellGetContext(pc, (void**)&mypc);/* Implement your preconditioner operation hereTypically computes y = M?1x where M is your preconditioner */return 0;
   }
   

4. Register and use your preconditioner:

   PC pc;
   KSPGetPC(ksp, &pc);MyPC *mypc;
   PetscNew(&mypc);PCSetType(pc, PCSHELL);
   PCShellSetContext(pc, mypc);
   PCShellSetSetUp(pc, MyPCSetup);
   PCShellSetApply(pc, MyPCApply);
   

Advanced Features

You can also set additional functions:

// For symmetric preconditioners
PCShellSetSymmetric(pc, PETSC_TRUE);// Set a function to view your preconditioner's info
PCShellSetView(pc, MyPCView);// Set a destroy function to clean up
PCShellSetDestroy(pc, MyPCDestroy);

Example: Diagonal Preconditioner

Here’s a complete example of a simple diagonal preconditioner:

typedef struct {Vec diagonal;  // stores the inverse diagonal
} DiagPC;static PetscErrorCode DiagPCSetup(PC pc)
{DiagPC *dpc;PCShellGetContext(pc, (void**)&dpc);Mat A;PCGetOperators(pc, &A, NULL);MatCreateVecs(A, &dpc->diagonal, NULL);MatGetDiagonal(A, dpc->diagonal);VecReciprocal(dpc->diagonal);  // store inverse diagonalreturn 0;
}static PetscErrorCode DiagPCApply(PC pc, Vec x, Vec y)
{DiagPC *dpc;PCShellGetContext(pc, (void**)&dpc);VecPointwiseMult(y, x, dpc->diagonal);return 0;
}static PetscErrorCode DiagPCDestroy(PC pc)
{DiagPC *dpc;PCShellGetContext(pc, (void**)&dpc);VecDestroy(&dpc->diagonal);PetscFree(dpc);return 0;
}// Usage:
PC pc;
KSPGetPC(ksp, &pc);DiagPC *dpc;
PetscNew(&dpc);PCSetType(pc, PCSHELL);
PCShellSetContext(pc, dpc);
PCShellSetSetUp(pc, DiagPCSetup);
PCShellSetApply(pc, DiagPCApply);
PCShellSetDestroy(pc, DiagPCDestroy);

Tips

1. Use PCGetOperators() to access the matrix being preconditioned
2. For efficiency, precompute what you can in the setup phase
3. Use PCShellSetName() to give your preconditioner a descriptive name
4. Consider implementing PCShellSetFromOptions() if your preconditioner has configurable parameters

Remember that PCShell gives you complete control over the preconditioner operation, but you’re responsible for implementing it efficiently.

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資料

PCRegister
PCSHELL