Adaptive grid refinement - PowerPoint PPT Presentation

Loading...

PPT – Adaptive grid refinement PowerPoint presentation | free to download - id: 144903-ODA5Y



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Adaptive grid refinement

Description:

Non-overlapping partition. Controllable addition of overlap (if desired) ... DD on non-matching subgrids. Example two. Laplace equation. Measurements for example two ... – PowerPoint PPT presentation

Number of Views:49
Avg rating:3.0/5.0
Slides: 24
Provided by: ksameu
Learn more at: http://heim.ifi.uio.no
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Adaptive grid refinement


1
Adaptive grid refinement
2
Adaptivity in Diffpack
  • Error estimator
  • Adaptive refinement
  • A hierarchy of unstructured grids
  • Solution method Multigrid, often optimal
    complexity
  • As an add-on Diffpack library

3
Parallel Computing in Diffpack
4
Two parallelization approaches
  • Flexible, user-friendly, extensible
  • Linear-algebra-level parallelization
  • An add-on library of parallel matrix/vector
    operations
  • Rapid transition from sequential simulator to
    parallel simulator
  • Simulator-parallel approach
  • High-level parallelization of multilevel methods
  • Extensive reuse of original sequential simulator
    in subdomain solves
  • A generic implementation framework

5
Grid partition
  • Basis for computation work decomposition
  • General treatment of unstructured grids
  • Arbitrary number of procs determined at run-time
  • Non-overlapping partition
  • Controllable addition of overlap (if desired)
  • Good load balancing - high parallel efficiency

6
Partition example
7
Linear-algebra-level parallelization
  • Easy to use
  • access to all existing Diffpack iterative
    methods, preconditioners and convergence monitors
  • need only to add a few lines of new code
  • arbitrary choice of number of procs at run-time
  • Parallel matrix/vector operations
  • inner-product of two vectors
  • matrix-vector product
  • preconditioning - block contribution from subgrids

8
Example one
  • Highly unstructured grid
  • Discontinuity in the coefficient

9
Measurements for example one
  • 130,561 degrees of freedom
  • Overlapping subgrids
  • BiCGStab (block) RILU prec.

10
An observation
  • The hope among early domain decomposition
    workers was that one could write a simple
    controlling program which would call the old PDE
    software directly to perform the subdomain
    solves. This turned out to be unrealistic because
    most PDE packages are too rigid and inflexible.
  • - Smith, Bjørstad
    and Gropp
  • The remedy
  • Correct use of object-oriented programming
    techniques.

11
Approach 2 simulator-parallel
  • Parallelization of multilevel methods
  • One subdomain is assigned with a sequential
    simulator
  • A generic implementation framework
  • Systematic and flexible
  • O-O programming enables extensive code reuse
  • Easy to incorporate multilevel algorithm
    modification
  • Different grid types, local solution methods etc.
    on different subdomains
  • DD on non-matching subgrids

12
Example two
Laplace equation
13
Measurements for example two
  • BiCGStab - global iterative solution method
  • Parallel DD as preconditioner
  • MG as subdomain solver
  • Overlapping subgrids

14
Measurements for example two
  • BiCGStab - global iterative solution method
  • One parallel MG iteration as preconditioner
  • Overlapping subgrids

15
Scalability
Measurements obtained on 16 processors
16
Example three
17
Measurements for example three
  • BiCGStab - global iterative solution method
  • One parallel MG iteration as preconditioner
  • Overlapping subgrids

18
2-phase porous media flow
19
2-phase porous media flow
SEQ
PEQ
Multigrid V-cycle in subdomain solves
20
Nonlinear water waves
  • Fully nonlinear 3D water waves
  • Primary unknowns

21
Parallel simulation of water waves
22
Parallel efficiency
  • Fixed number of subdomains M16.
  • Subdomain grids from partition of a global
    41x41x41 grid.
  • Simulation over 32 time steps.
  • DD as preconditioner of CG for the Laplace eq.
  • Multigrid V-cycle as subdomain solver.

23
Overall efficiency
  • Number of subdomains equal to number of
    processors

For P2 parallel BiCGStab is used.
About PowerShow.com