TY - JOUR

T1 - The surrogate matrix methodology

T2 - Low-cost assembly for isogeometric analysis

AU - Drzisga, Daniel

AU - Keith, Brendan

AU - Wohlmuth, Barbara

N1 - Publisher Copyright:
© 2019 Elsevier B.V.

PY - 2020/4/1

Y1 - 2020/4/1

N2 - A new methodology in isogeometric analysis (IGA) is presented. This methodology delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed from element-scale quadrature formulas. To generate surrogate matrices, quadrature must only be performed on certain elements in the computational domain. This, in turn, determines only a subset of the entries in the final matrix. The remaining matrix entries are computed by a simple B-spline interpolation procedure. Poisson's equation, membrane vibration, plate bending, and Stokes’ flow problems are studied. In these problems, the use of surrogate matrices has a negligible impact on solution accuracy. Because only a small fraction of the original quadrature must be performed, we are able to report beyond a fifty-fold reduction in overall assembly time in the same software. The capacity for even further speed-ups is clearly demonstrated. The implementation used here was achieved by a small number of modifications to the open-source IGA software library GeoPDEs. Similar modifications could be made to other present-day software libraries.

AB - A new methodology in isogeometric analysis (IGA) is presented. This methodology delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed from element-scale quadrature formulas. To generate surrogate matrices, quadrature must only be performed on certain elements in the computational domain. This, in turn, determines only a subset of the entries in the final matrix. The remaining matrix entries are computed by a simple B-spline interpolation procedure. Poisson's equation, membrane vibration, plate bending, and Stokes’ flow problems are studied. In these problems, the use of surrogate matrices has a negligible impact on solution accuracy. Because only a small fraction of the original quadrature must be performed, we are able to report beyond a fifty-fold reduction in overall assembly time in the same software. The capacity for even further speed-ups is clearly demonstrated. The implementation used here was achieved by a small number of modifications to the open-source IGA software library GeoPDEs. Similar modifications could be made to other present-day software libraries.

KW - A priori error analysis

KW - Assembly

KW - Isogeometric analysis

KW - Surrogate numerical methods

UR - http://www.scopus.com/inward/record.url?scp=85077020710&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2019.112776

DO - 10.1016/j.cma.2019.112776

M3 - Article

AN - SCOPUS:85077020710

SN - 0045-7825

VL - 361

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

M1 - 112776

ER -