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Iterative Sectioning of High Dimensional Banded Matrices

Iterative Sectioning of High Dimensional Banded Matrices. Dmytro Fedasyuk, Pavlo Serdyuk, Yuriy Semchyshyn Software Department Lviv Polytechnic National University. Problem Statement: SLE. Problem Statement: Sectioning. Problem Statement: Example. Quality Criteria: Sectioning Smallness.

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Iterative Sectioning of High Dimensional Banded Matrices

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  1. Iterative Sectioning of High Dimensional Banded Matrices Dmytro Fedasyuk, Pavlo Serdyuk, Yuriy Semchyshyn Software Department Lviv Polytechnic National University

  2. Problem Statement: SLE

  3. Problem Statement: Sectioning

  4. Problem Statement: Example

  5. Quality Criteria: Sectioning Smallness

  6. Quality Criteria: Sectioning Accuracy

  7. Quality Criteria: Results Precision

  8. Iterative (IT) Sectioning Algorithm • Get the initial sectioning using Bidirectional (BD) or Adjustable (AD) algorithm. • Iterate through all sections, from the first to the last, in case if one of them can be split into two separate sections — split this section. • Iterate through all pairs of consecutive sections from the first to the last, in case if some sections can be balanced by detaching some elements from larger of them and attaching to smaller — balance these sections. • If there is at least one splitting or balancing done while performing previous two steps — go to step IT2. • Return the result.

  9. Experiment: Test Matrices

  10. Experiment: Results (Table)

  11. Experiment: Results (Charts) Sectioning Smallness Sectioning Accuracy

  12. Application: Fixed Partial Denture

  13. Application: FEM and Matrix

  14. Application: Results Bidirectional (BD) Sectioning Algorithm Iterative (IT) Sectioning Algorithm

  15. Questions?

  16. Thank You!

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