ScaLAPACK

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Introduction to the ACTS Collection Why/How Do We
Use These Tools?
Tony Drummond Computational Research
Division Lawrence Berkeley National
Laboratory University of California, Berkeley -
CS267 April 20, 2006 - Berkeley, California
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Lesson High Quality Software Reusability
Introduction to The ACTS Collection
Hardware - Middleware - Firmware
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ACTS Numerical Tools Functionality
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ACTS Numerical Tools Functionality
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Structure of PETSc
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Hypre Conceptual Interfaces
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Hypre Conceptual Interfaces
INTERFACE TO SOLVERS
List of Solvers and Preconditioners per
Conceptual Interface
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ACTS Numerical Tools Functionality
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ACTS Numerical Tools Functionality
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ACTS Numerical Tools Functionality
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ACTS Numerical Tools Functionality
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ACTS Numerical Tools Functionality
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TAO - Interface with PETSc
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OPT Interfaces

• Four major classes of problems available
• NLF0(ndim, fcn, init_fcn, constraint)
• Basic nonlinear function, no derivative
  information available
• NLF1(ndim, fcn, init_fcn, constraint)
• Nonlinear function, first derivative information
  available
• FDNLF1(ndim, fcn, init_fcn, constraint)
• Nonlinear function, first derivative information
  approximated
• NLF2(ndim, fcn, init_fcn, constraint)
• Nonlinear function, first and second derivative
  information available

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ACTS Numerical Tools Functionality
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ACTS Numerical Tools Functionality
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ACTS Numerical Tools Functionality
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ACTS Numerical Tools Functionality
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User Interfaces
Introduction to The ACTS Collection
Command lines
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User Interfaces
Introduction to The ACTS Collection
PyACTS
Ax b
matlabP
Star-P
View_field(T1)
User
NetSolve
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Tool Interoperability Tool-to-Tool
TOOL B
TOOL C
TOOL A
TOOL F
TOOL E
TOOL D
Trilinos
Ex 3
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Component Technology!
Tool C
Tool A
Tool D
Tool B
ESI
CCA
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Introduction to PETSc

• Introducción a PETSC
• Vectors
• Matrices
• PETSc viewers
• Use of Preconditioners in PETSc
• Some examples using PETSc

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What is PETSc?
PETSc Portable Extensible Toolkit for Scientific
Computation

• Developed at Argonne National Laboratory
• Library that supports work with PDE
• Public Domain
• Portable to a variety of platforms
• Project started in 1991.
• Written in C with a fortran interface and OO
  flavor

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Nonlinear Solvers
Time Steppers
Newton-based Methods
Other
Euler
Backward Euler
Pseudo Time Stepping
Other
Line Search
Trust Region
Krylov Subspace Methods
Richardson
Chebychev
Other
GMRES
CG
CGS
Bi-CG-STAB
TFQMR
Preconditioners
Additive Schwartz
Block Jacobi
Jacobi
ILU
ICC
LU (Sequential only)
Others
Matrices
Compressed Sparse Row (AIJ)
Blocked Compressed Sparse Row (BAIJ)
Block Diagonal (BDIAG)
Dense
Other
Matrix-free
Distributed Arrays
Index Sets
Indices
Block Indices
Stride
Other
Vectors
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Vectors Fundamental Objects to store fields,
right-hand side vectors, etc. .
Matrices Fundamental Objects to store operators
(like Jacobians)
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• Each process owns a piece of the vector
• VECTOR Types Sequential, MPI or SHARED

• VecCreate(MPI_Comm Comm,Vec v)
• comm - MPI_Comm parallel processes
• v vector
• VecSetType(Vec,VecType)
• Valid Types are
• VEC_SEQ, VEC_MPI, o VEC_SHARED
• VecSetSizes(Vec v,int n, int N)
• Where n or N (not both) can be
• PETSC_DECIDE
• VecDestroy(Vec )

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PETSc - Vector Example (in C)
include petscvec.h int main(int argc,char
argv) Vec x
int n 20,m4, ierr
PetscInitialize(argc,argv)
VecCreate(PETSC_COMM_WORLD,x)
VecSetSizes(x,PETSC_DECIDE,n)
VecSetFromOptions(x) lt-- USER_CODEWork with
PETSc VECTOR --gt PetscFinalize()
return 0
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• Types
• default sparse AIJ MPIAIJ, SEQAIJ
• block sparse AIJ (for multi-component PDEs)
  MPIAIJ, SEQAIJ
• symmetric block sparse AIJ MPISBAIJ, SAEQSBAIJ
• block diagonal MPIBDIAG, SEQBDIAG
• dense MPIDENSE, SEQDENSE
• matrix-free

• MatCreate(MPI_Comm Comm, Mat A)
• MPI_Comm - group of process that work on A
• MatSetSizes(Mat A, PetscInt m, PetscInt n,
  PetscInt M, PetscInt N)
• MatSetType(Mat,MatType)
• MatDestroy(Mat)

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• Single user interface to matrices (operators)
• Input values to a PETSc matrix
• MatSetValues(Mat mat,PetscInt m,const PetscInt
  idxm,PetscInt n,const PetscInt idxn,const
  PetscScalar v,InsertMode addv)
• Matriz-vector multiplication
• For instance MatMult(A,y,x) (y?x)
• Matrix viewing
• MatView()
• Multiple underlying implementations
• AIJ, block AIJ, symmetric block AIJ, block
  diagonal, dense, matrix-free, etc.

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Block-Row distribution per process
M8,N8,m3,nk1 rstart0,rend4
proc 1
M8,N8,m3,nk2 rstart3,rend6
proc 2
M8,N8,m2,n k3 rstart6,rend8
proc 3

• The values of k1, k2 y k3 depend on the
  application and must be compatible with vector x
  (Axb)
• MatGetOwnershipRange(Mat A, int rstart, int
  rend)
• rstart first global row number that belongs
  to a process
• rend -1 Last row global number that belongs to
  a process

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PETSc Matrix Example

• Included in PETSc Distribution
• PETSC_DIR/src/mat/tutorial/ex2.c
• PETSC_DIR/src/mat/tutorial/ex5.c

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• Obtain basic information on PETSc viewers
• Run time options
• Extract data that can be later use by other
  packages/app. programs.
• vector fields, matrix contents
• various formats (ASCII, binary)
• Visualization
• simple graphics created with X11 to display
  vector campo, non-zero element structure of a
  matrix, etc.

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• MatView(Mat A, PetscViewer v)
• Runtime options available after matrix assembly
• -mat_view_info Information related to matrix type
• -mat_view_draw nonzero pattern
• -mat_view
• data in ASCII
• etc.

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Examples of Viewers and Matrices

• Included in PETSc Distribution
• PETSC_DIR/src/mat/tests/ex2.c
• Using the -mat_view_info_detailed, etc
• PETSC_DIR/src/mat/tests/ex3.c
• Using the -mat-view-draw

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• Objective Support the solution of Linear System
  of the form,
• Axb,
• Krylov Subspace methods are highly dependent of
  the spectrum of the matrix A. The use of
  preconditioners can speed-up their convergence.

KRYLOV SUBSPACE METHODS PRECONDITIONERS R.
Freund, G. H. Golub, and N. Nachtigal. Iterative
Solution of Linear Systems,pp 57-100. ACTA
Numerica. Cambridge University Press, 1992.
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• Axb,

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Main Routine
PETSc
Linear Solvers (SLES)
Solve Ax b
PC
KSP
Application Initialization
Evaluation of A and b
Post- Processing
PETSc code
User code
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Krylov Methods (KSP)
Preconditioners (PC)

• Block Jacobi
• Overlapping Additive Schwarz
• ICC, ILU via BlockSolve95
• ILU(k), LU
• etc.

• Conjugate Gradient
• GMRES
• CG-Squared
• Bi-CG-stab
• Transpose-free QMR
• Chebychev
• CGNE
• Many more (check manual)

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Time Stepper Types (TS)
TS_EULER - Euler TS_SUNDIALS- SUNDIALS
interface TS_BEULER - Backward Euler TS_PSEUDO-
Pseudo-timestepping