Multipatch Space-Time Isogeometric Analysis of Parabolic Diffusion Problems

2018 ◽  
pp. 21-32 ◽  
Author(s):  
U. Langer ◽  
M. Neumüller ◽  
I. Toulopoulos
Keyword(s):  
Isogeometric Analysis ◽  
Space Time ◽  
Diffusion Problems

Space‐Time Isogeometric Analysis of Parabolic Diffusion Problems in Moving Spatial Domains

PAMM ◽  
2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Svetlana Kyas ◽  
Ulrich Langer ◽  
Sergey Repin
Keyword(s):  
Isogeometric Analysis ◽  
Space Time ◽  
Spatial Domains ◽  
Diffusion Problems

scholarly journals Isogeometric analysis in advection–diffusion problems: Tension splines approximation

2011 ◽  
Vol 236 (4) ◽  
pp. 511-528 ◽  
Author(s):  
Carla Manni ◽  
Francesca Pelosi ◽  
M. Lucia Sampoli
Keyword(s):  
Isogeometric Analysis ◽  
Advection Diffusion ◽  
Diffusion Problems

Analysis of space–time discontinuous Galerkin method for nonlinear convection–diffusion problems

2010 ◽  
Vol 117 (2) ◽  
pp. 251-288 ◽  
Author(s):  
Miloslav Feistauer ◽  
Václav Kučera ◽  
Karel Najzar ◽  
Jaroslava Prokopová
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Space Time ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
Diffusion Problems

scholarly journals Low-Rank Space-Time Decoupled Isogeometric Analysis for Parabolic Problems with Varying Coefficients

2019 ◽  
Vol 19 (1) ◽  
pp. 123-136 ◽  
Author(s):  
Angelos Mantzaflaris ◽  
Felix Scholz ◽  
Ioannis Toulopoulos
Keyword(s):  
Isogeometric Analysis ◽  
Evolution Equations ◽  
Space Time ◽  
Point Of View ◽  
Low Rank ◽  
Parabolic Problems ◽  
Computational Point ◽  
Varying Coefficients ◽  
Analysis Scheme ◽  
Parabolic Evolution Equations

AbstractIn 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 {\mathbb{R}^{d+1}}, with {d=2,3}, 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.

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