The enhanced derived-vector-space approach to domain decomposition methods
Ismael Herrera Revilla (Instituto de Geof\'isica Universidad Nacional, Aut\'onoma de M\'exico (UNAM))
TL;DR
This paper introduces an improved derived-vector-space (DVS) method for domain decomposition that overcomes previous limitations by eliminating the need for special matrices, making it applicable to a broader class of linear problems.
Contribution
An enhanced DVS formulation is proposed, removing the requirement for constructing special matrices and extending applicability to all linear problems.
Findings
The new DVS approach is applicable to any linear problem.
It produces block-diagonal system matrices.
The method improves parallel processing efficiency.
Abstract
Standard approaches to domain decomposition methods (DDM) are uncapable of producing block-diagonal system matrices. The derived-vector-space (DVS), approach to DDM, introduced in 2013, overcomes this limitation. However, the DVS approach in its original form was applicable to a relatively narrow class of problems because it required building a special matrix, whose construction is frequently impossible. In this paper, an enhanced formulation of DVS is presented, which does not require the construction of a special matrix and is applicable to any linear problem. Keywords: domain decomposition, parallel processing, DVS, FETI, BDDC
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Model Reduction and Neural Networks · Electromagnetic Simulation and Numerical Methods