DeepAI AI Chat
Log In Sign Up

Isogeometric Residual Minimization Method (iGRM) with Direction Splitting Preconditoner for Stationary Advection-Diffusion Problems

by   Marcin Łoś, et al.
Pontificia Universidad Católica de Valparaíso
Curtin University

In this paper, we propose the Isogeometric Residual Minimization (iGRM) with direction splitting. The method mixes the benefits resulting from isogeometric analysis, residual minimization, and alternating direction solver. Namely, we utilize tensor product B-spline basis functions and alternating direction methods. We apply a stabilized mixed method based on residual minimization. We propose a preconditioned conjugate gradients method with a linear computational cost resulting from a Kronecker product structure of the system of linear equations. We test our method on two-dimensional simulations of advection-diffusion problems, including the problem with the manufactured solution, the Eriksson-Johnson problem, and a rotating flow problem. We compare our method to the Discontinuous Petrov-Galerkin and the Streamline Upwind Petrov-Galerkin (SUPG) stabilization methods. The resulting method is not restricted to a Kronecker product structure of the diffusion or advection data.


page 14

page 16

page 18

page 21


Isogeometric Residual Minimization Method (iGRM) with Direction Splitting for Non-Stationary Maxwell Problems

We focus on non-stationary Maxwell equations defined on a regular patch ...

Isogeometric Residual Minimization Method (iGRM) for Stokes and Time-Dependent Stokes Problems

We investigate the application of the residual minimization method (RM) ...

A nonlinear weak constraint enforcement method for advection-dominated diffusion problems

We devise a stabilized method to weakly enforce bound constraints in the...

Eliminating Gibbs Phenomena: A Non-linear Petrov-Galerkin Method for the Convection-Diffusion-Reaction Equation

In this article we consider the numerical approximation of the convectio...

Direction splitting of φ-functions in exponential integrators for d-dimensional problems in Kronecker form

In this manuscript, we propose an efficient, practical and easy-to-imple...

Multigrid preconditioning of singularly perturbed convection-diffusion equations

Boundary value problems based on the convection-diffusion equation arise...