2023/12/14 by Monica Montardini, Montardini, Monica, Giancarlo Sangalli +3 · 2 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2312.08736
openalex publication_date 2023/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose an innovative isogeometric low-rank solver for the linear elasticity model problem, specifically designed to allow multipatch domains. Our approach splits the domain into subdomains, each formed by the union of neighboring patches. Within each subdomain, we employ Tucker low-rank matrices and vectors to approximate the system matrices and right-hand side vectors, respectively. This enables the construction of local approximate fast solvers. These local solvers are then combined into an overlapping Schwarz preconditioner, which is utilized in a truncated preconditioned conjugate gradient method. Numerical experiments demonstrate the significant memory storage benefits and a uniformly bounded number of iterations with respect to both mesh size and spline degree.