Concepts for implementing adaptive finite element codes for grid computing

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Concepts for implementing adaptive finite element
codes for grid computing

• Krzysztof Banas, Joanna Plazek
• Cracow University of Technology
• Krzysztof.Banas_at_pk.edu.pl

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Outline

• Motivation
• FEM code as grid application
• Current project
• Future plans

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Grid environment from application developer
perspective

• Open environment (coupling with external modules,
  standardization of interfaces)
• High performance communication libraries
• Simpler code development
• Cooperation with other groups
• Broad user base

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State of the art for the FEM

• Complex problems (nonlinear, coupled,
  multi-scale, multi-physics)
• Complex codes (adaptive meshes, multi-level
  solvers, parallel and distributed execution)
• Steep learning curves for users
• Unmanageable software for developers

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Example finite element PSE

• Preprocessing
• geometrical modeling
• mesh generation

Computational Module
ODE integration
GUI interactive visualization, collaboration
and steering
linear solver
field discretization
adaptive mesh services
Postprocessing
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Current project - existing software

• Adaptive FE codes in Fortran 77, Fortran 90, C
• Areas of application acoustics, elasticity,
  compressible fluid flow, multi-phase flow,
  electro-magnetism
• hp-adaptivity
• Multi-level solvers
• Parallel versions for PVM, DSM and MPI

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Current project - application areas

• Scattering of acoustic and
• electro-magnetic waves

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Current project - application areas

• Subsurface flow simulation
• (discontinuous approximation,
• multi-level solvers)

Table1. Number of linear solver iterations to
reach convergence
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Current project - application areas

• Compressible fluid flow

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Current project

• Modularization
• Standardization of interfaces
• Testing communication mechanisms
• Coupling with visualization software

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FE code modules

• Assumptions
• code is built from small specialized modules
• modules form separate libraries
• modules have their own data structure
• interfaces are designed for F90, C and C
• modules may define their own data distribution
• modules are glued together by problem dependent
  code

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FE code modules

• Adaptive mesh procedures
• Read_mesh_data( mesh_id, read_type)
• Create_node(mesh_id, parameters, node_id)
• Divide_element(mesh_id, element_id,
  element_sons_ids)
• Get_element_father(mesh_id, element_id,
  father_id)
• Get_face_edges(mesh_id, face_id,
  face_edges_ids)
• Get_element_neighbors(mesh_id, element_id,
  neighbors_ids)
• ...

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FE code modules

• Field discretization procedures
• Get_face_dofs( field_id, face_id, dofs)
• L2_project_dofs_from_element_to_element(
• field_id, element_from_id, element_to_id)
• Get_solution_at_point( field_id,
  point_coordinates, solution)
• Set_uniform_degree_p( field_id)
• Write_element_solution( field_id, element_id,
  solution_dofs)
• ...

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FE code modules

• Linear equations solver procedures
• Set_preconditioner_options(solver_id,
  preconditioner_type, preconditioner_parame
  ters)
• Assemble_element_stiffness_matrix( solver_id,
  assembly_type,
• block_sizes, block_positions, stiffness
  matrices, load_vectors)
• Solve_system(solver_id)
• Store_face_solution( solver_id, face_id, dofs)
• Free_solver_memory(solver_id)
• ...

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Why adaptive FE code can be attractive as grid
application?

• Powerful tool for scientific and engineering
  analysis
• Complex, multi-component code
• Large amounts of data produced and exchanged
  among modules
• Adaptive meshes require adaptive resources

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Future plans

• Open, flexible, extensible FE software
• Large-scale distributed computing
• Integrated problem solving environment

• Sky is the limit...