TY - JOUR

T1 - Isogeometric Residual Minimization Method (iGRM) with direction splitting for non-stationary advection–diffusion problems

AU - Łoś, M.

AU - Muñoz-Matute, J.

AU - Muga, I.

AU - Paszyński, M.

N1 - Publisher Copyright:
© 2019 Elsevier Ltd

PY - 2020/1/15

Y1 - 2020/1/15

N2 - In this paper, we propose a novel computational implicit method, which we call Isogeometric Residual Minimization (iGRM) with direction splitting. The method mixes the benefits resulting from isogeometric analysis, implicit dynamics, residual minimization, and alternating direction solver. We utilize tensor product B-spline basis functions in space, implicit second order time integration schemes, residual minimization in every time step, and we exploit Kronecker product structure of the matrix to employ linear computational cost alternating direction solver. We implement an implicit time integration scheme and apply, for each space-direction, a stabilized mixed method based on residual minimization. We show that the resulting system of linear equations has a Kronecker product structure, which results in a linear computational cost of the direct solver, even using implicit time integration schemes together with the stabilized mixed formulation. We test our method on three advection–diffusion computational examples, including model “membrane” problem, the circular wind problem, and the simulations modeling pollution propagating from a chimney.

AB - In this paper, we propose a novel computational implicit method, which we call Isogeometric Residual Minimization (iGRM) with direction splitting. The method mixes the benefits resulting from isogeometric analysis, implicit dynamics, residual minimization, and alternating direction solver. We utilize tensor product B-spline basis functions in space, implicit second order time integration schemes, residual minimization in every time step, and we exploit Kronecker product structure of the matrix to employ linear computational cost alternating direction solver. We implement an implicit time integration scheme and apply, for each space-direction, a stabilized mixed method based on residual minimization. We show that the resulting system of linear equations has a Kronecker product structure, which results in a linear computational cost of the direct solver, even using implicit time integration schemes together with the stabilized mixed formulation. We test our method on three advection–diffusion computational examples, including model “membrane” problem, the circular wind problem, and the simulations modeling pollution propagating from a chimney.

KW - Advection-diffusion simulations

KW - Implicit dynamics

KW - Isogeometric analysis

KW - Linear computational cost

KW - Residual minimization

KW - Second order time integration schemes

UR - http://www.scopus.com/inward/record.url?scp=85068395014&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2019.06.023

DO - 10.1016/j.camwa.2019.06.023

M3 - Article

AN - SCOPUS:85068395014

SN - 0898-1221

VL - 79

SP - 213

EP - 229

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 2

ER -