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Review (Chapter 2)

  • Review of the Literature
    • RBF Algorithms
    • GPU for PDEs
    • GPU for RBF
    • Explicit/Implicit RBF
    • Explicit/Implicit RBF-FD
    • Implicit GPU
  • Compare contrast and evaluate previous publications.

Introduction (Chapter 1)

  • Need motivation for research
  • Background of the problem/study
    • High level; will get into detail in related work section
  • Statement of the problem
  • High level research questions
    • Possible to prepare for the transition to exa-scale computing? What is necessary?
    • What algorithms or data-structures would be necessary?
  • Importance of the study (why should the reader care)?
  • Scope of the study?
    • What is not within the scope?
      • we don't focus entirely on the problem of optimizing GPU kernels as our problem leverages higher level matrix algebra primitives (spmv, saxpy, gemm)
      • we don't worry about domain partitioning (leave it to METIS), but we do worry about load balancing communication (overlap comm and comp).
    • Do worry about node ordering
    • Do worry about node indexing
    • Do worry about explicit/implicit solvers
    • Do worry about applications
  • Definition of Terms
    • node
    • stencil
    • center
    • weight
    • rbf
    • gpu
    • partition
  • Limitations
    • Limited GPU kernels (solver only takes advantage of the GPU)
    • Balanced MPI, OpenCL, GPU Library, and Application studies.
    • Not as advanced as PETsc, Deal.ii, Trilinos, etc. which all have 10+ years of development

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