Description
Title: ARABIC PROBLEMS LINEAR COMPUTATIONAL COST IMPLICIT SOLVER
Abstract: In this study, we simulate transient issues using the isogeometric nite elements and the alternating direction method. We specifically concentrate on a parabolic problem and fully discretize it using implicit time-marching and space B-spline basis functions. In order to separate our differential operator into a summation of the blocks acting along a specific coordinate axis in the intermediate time-steps, we introduce intermediate time-steps. We demonstrate that the resulting stiffness matrix can be represented as the product of two (in 2D) or three (in 3D) multi-diagonal matrices, each of which has B-spline basis functions along a different axis of the spatial coordinate system. These algebraic transformations give us a set of linear equations that can be factored at each time-step of the implicit method with a linear O(N) computational cost. We simulate the heat transfer issue using our method. We show theoretically and numerically that the unconditional stability of our implicit method for heat transfer problems (i.e., parabolic). We talk about the method’s limitations as we wrap up our presentation.
Keywords: isogeometric analysis, implicit dynamics, linear computational cost, direct solvers
Paper Quality: SCOPUS / Web of Science Level Research Paper
Paper type: Analysis Based Research Paper
Subject: Computer Science
Writer Experience: 20+ Years
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