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arXiv · 1809.10026

Space-time least-squares isogeometric method and efficient solver for parabolic problems

Monica Montardini·Matteo Negri·Giancarlo Sangalli·Mattia Tani
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Abstract

In this paper, we propose a space-time least-squares isogeometric method to solve parabolic evolution problems, well suited for high-degree smooth splines in the space-time domain. We focus on the linear solver and its computational efficiency: thanks to the proposed formulation and to the tensor-product construction of space-time splines, we can design a preconditioner whose application requires the solution of a Sylvester-like equation, which is performed efficiently by the fast diagonalization method. The preconditioner is robust w.r.t. spline degree and mesh size. The computational time required for its application, for a serial execution, is almost proportional to the number of degrees-of-freedom and independent of the polynomial degree. The proposed approach is also well-suited for parallelization.

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Monica Montardini, Matteo Negri, Giancarlo Sangalli, Mattia Tani. 2018-09-26. Space-time least-squares isogeometric method and efficient solver for parabolic problems. https://arxiv.org/abs/1809.10026

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