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Mathematical Foundations of High-Performance Computing and Communications (1991) / Chapter Skim
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5 SUMMARY OF THE AREAS WHERE NEW MATHEMATICAL SCIENCES RESEARCH IS NEEDED
Pages 27-28

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From page 27...
... Numerical algorithms, especially multigrid and domain decomposition methods and parallel algorithms, and adaptive mesh generation for partial differential equations, as they arise in modeling semiconductors, geophysics, turbulence, and elsewhere; . Homogenization methods, as they arise in the modeling of oil reservoirs and the atmosphere, in materials science, and in any situation where the range of relevant length scales exceeds our capability to resolve them by brute-force computations; .
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From page 28...
... It is vital that, as the overall research effort in high-performance computing and communications is stepped up, relevant areas of the mathematical sciences also receive commensurate attention and support.
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Key Terms

  • differential equations
  • uncertainty based
  • modeling semiconductors
  • domain decomposition
  • decomposition methods

  • numerical algorithms
  • commensurate attention
  • dynamic programming
  • partial differential
  • overall research

  • studying global
  • scales exceeds
  • parallel algorithms
  • numerical experiments
  • pattern matching

  • mesh generation
  • model validation
  • efficient pattern
  • relevant length
  • length scales

  • homogenization methods
  • including dynamic
  • physical experiments
  • receive commensurate
  • experiments combined

  • oil reservoirs
  • especially multigrid
  • adaptive mesh
  • materials science
  • network flow


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