| EPSRC Reference: |
GR/R46427/01 |
| Title: |
Direct and iterative methods for solving augmented systems related to mixed finite element methods. |
| Principal Investigator: |
Duff, Professor I |
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| Department: |
Computational Science & Engineering |
| Organisation: |
STFC Laboratories (Grouped) |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 June 2001 |
Ends: |
30 September 2001 |
Value (£): |
4,400
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The solution of large sparse augmented systems of equations arises in many scientific and engineering problems. For example, the approximation of Darcy's Laws by Mixed Finite Element techniques produces a finite dimensional version of the continuous problem which is described by an augmented system. We hope to address two main issues:Firstly, the strong relationship between the mixed-hybrid finite-element approximation and special augmented matrices, where a submatrix is a totally unimodular matrix related to the mesh graph, suggests the possibility of building fast decomposition methods based on classical network programming algorithms. We plan to combine shortest path tree algorithms with re-ordering methods such as minimum degree or nested dissection. This will allow us to investigate the design of a prototype package for the more general problem of the minimization of nonlinear convex functions in many variables over a network. Because of the very large number of unknowns in such problems, we intend to investigate the use of hybrid techniques based on nullspace algorithms and the conjugate gradient method. Secondly, we intend to analyse new stopping criteria for iterative methods applied to the solution of the linear algebraic systems arising in partial differential equation approximation.
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Key Findings |
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Potential use in non-academic contexts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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