THE DERIVED-VECTOR-SPACE: A UNIFIED FRAMEWORK FOR NONOVERLAPPING DDM

THE DERIVED-VECTOR-SPACE: A UNIFIED FRAMEWORK FOR NONOVERLAPPING DDM

Herrera, I.

Full Article:

We present and discuss a framework called the ‘derived-vector-space (DVS) framework’. In part, the relevance of this framework is because in its realm four preconditioned massively parallelizable DVS-algorithms with constraints of general applicability (by this we mean: applicable to symmetric-definite, non-symmetric and indefinite matrices) have been developed. Such algorithms yield codes that are almost 100% in parallel; more precisely, they achieve what we call the ‘leitmotif of DDM research’: to obtain algorithms that yield the global solution by solving local problems exclusively. This has been possible because in the DVS-approach the original PDE, or system of such equations, is transformed into a problem formulated in the derived-vector-space, which is a Hilbert-space that is well-defined by itself independently of the particular PDE considered, and afterwards all the numerical work is done in that space. Thus, the applicability of the algorithms developed in this framework is essentially independent of the specific problem considered, and furthermore this allows the development of codes, which to a large extent are of universal applicability. Thus, the DVSalgorithms are very suitable for programming in an efficient manner the most powerful parallel computers available at present.

We present and discuss a framework called the ‘derived-vector-space (DVS) framework’. In part, the relevance of this framework is because in its realm four preconditioned massively parallelizable DVS-algorithms with constraints of general applicability (by this we mean: applicable to symmetric-definite, non-symmetric and indefinite matrices) have been developed. Such algorithms yield codes that are almost 100% in parallel; more precisely, they achieve what we call the ‘leitmotif of DDM research’: to obtain algorithms that yield the global solution by solving local problems exclusively. This has been possible because in the DVS-approach the original PDE, or system of such equations, is transformed into a problem formulated in the derived-vector-space, which is a Hilbert-space that is well-defined by itself independently of the particular PDE considered, and afterwards all the numerical work is done in that space. Thus, the applicability of the algorithms developed in this framework is essentially independent of the specific problem considered, and furthermore this allows the development of codes, which to a large extent are of universal applicability. Thus, the DVSalgorithms are very suitable for programming in an efficient manner the most powerful parallel computers available at present.

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DOI: 10.5151/meceng-wccm2012-18051

Referências bibliográficas

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Como citar:

Herrera, I.; "THE DERIVED-VECTOR-SPACE: A UNIFIED FRAMEWORK FOR NONOVERLAPPING DDM", p-651-658. In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 23580828, DOI 10.5151/meceng-wccm2012-18051