Fast Space-time IsoGeometric solvers for nonlinear transient heat transfer problems
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This paper explores the application of Space-Time IsoGeometric Analysis for solving nonlinear transient heat transfer problems and reviews numerical techniques aimed at enhancing computational efficiency. To address the nonlinear behavior of materials commonly encountered in industrial processes, we implement robust nonlinear solvers, including Newton’s and Picard’s methods. To mitigate the high computational costs and memory demands of space-time methods, we employ optimization strategies such as Matrix-Free and Weighted-Quadrature approaches. Additionally, we incorporate a Fast Diagonalization-based preconditioner to improve the efficiency of the iterative solver. Numerical experiments demonstrate the advantages of space-time methods over traditional incremental approaches, particularly when optimized algorithms are utilized. Our analysis also underscores the benefits of inexact nonlinear solvers in preventing oversolving and accelerating convergence. This study contributes to the development of efficient and scalable algorithms for nonlinear heat transfer problems.