TY - JOUR
T1 - Low-Rank Space-Time Decoupled Isogeometric Analysis for Parabolic Problems with Varying Coefficients
AU - Mantzaflaris, Angelos
AU - Scholz, Felix
AU - Toulopoulos, Ioannis
N1 - Funding Information:
This work was supported by the Austrian Science Fund (FWF) under the grant NFN S117.
Publisher Copyright:
© 2018 Walter de Gruyter GmbH, Berlin/Boston 2019.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - In this paper we present a space-time isogeometric analysis scheme for the discretization of parabolic evolution equations with diffusion coefficients depending on both time and space variables. The problem is considered in a space-time cylinder in Rd+1, with d = 2, and is discretized using higher-order and highly-smooth spline spaces. This makes the matrix formation task very challenging from a computational point of view. We overcome this problem by introducing a low-rank decoupling of the operator into space and time components. Numerical experiments demonstrate the efficiency of this approach.
AB - In this paper we present a space-time isogeometric analysis scheme for the discretization of parabolic evolution equations with diffusion coefficients depending on both time and space variables. The problem is considered in a space-time cylinder in Rd+1, with d = 2, and is discretized using higher-order and highly-smooth spline spaces. This makes the matrix formation task very challenging from a computational point of view. We overcome this problem by introducing a low-rank decoupling of the operator into space and time components. Numerical experiments demonstrate the efficiency of this approach.
KW - B-Splines Isogeometric Matrix Assembly
KW - Isogeometric Analysis
KW - Low-Rank Approximation
KW - Parabolic Initial-Boundary Value Problems
UR - http://www.scopus.com/inward/record.url?scp=85044712529&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85044712529&partnerID=8YFLogxK
U2 - 10.1515/cmam-2018-0024
DO - 10.1515/cmam-2018-0024
M3 - Article
AN - SCOPUS:85044712529
SN - 1609-4840
VL - 19
SP - 123
EP - 136
JO - Computational Methods in Applied Mathematics
JF - Computational Methods in Applied Mathematics
IS - 1
ER -