OVERLAPPING SCHWARZ METHODS FOR ISOGEOMETRIC ANALYSIS

We construct and analyze an overlapping Schwarz preconditioner for elliptic problems discretized with isogeometric analysis. The preconditioner is based on partitioning the domain of the problem into overlapping subdomains, solving local isogeometric problems on these subdomains, and solving an addi...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2012-01, Vol.50 (3), p.1394-1416
Main Authors: DA VEIGA, L. BEIRÃO, CHO, D., PAVARINO, L. F., SCACCHI, S.
Format: Article
Language:English
Subjects:
Applied mathematics
Approximation
Computer aided design
Computer analysis
Degrees of polynomials
Geometry
Knots
Mathematical functions
Mathematical vectors
Mathematics
Polynomials
Tensors
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Summary:We construct and analyze an overlapping Schwarz preconditioner for elliptic problems discretized with isogeometric analysis. The preconditioner is based on partitioning the domain of the problem into overlapping subdomains, solving local isogeometric problems on these subdomains, and solving an additional coarse isogeometric problem associated with the subdomain mesh. We develop an h-analysis of the preconditioner, showing in particular that the resulting algorithm is scalable and its convergence rate depends linearly on the ratio between subdomain and "overlap sizes" for fixed polynomial degree p and regularity k of the basis functions. Numerical results in two-and three-dimensional tests show the good convergence properties of the preconditioner with respect to the isogeometric discretization parameters h, p, k, number of subdomains N, overlap size, and also jumps in the coefficients of the elliptic operator.
ISSN:0036-1429
1095-7170
DOI:10.1137/110833476