New Math Tool Speeds Up Wave Simulations for Complex Engineering Problems
Researchers have developed a faster computational method for solving wave equations used in everything from seismic imaging to electromagnetic simulations. The breakthrough makes it possible to handle previously intractable real-world scenarios where wave properties vary unpredictably, potentially cutting computation time significantly for oil exploration, medical imaging, and telecommunications firms.
Originaltitel: Clustering/Distribution Analysis and Preconditioned Krylov Solvers for the Approximated Helmholtz Equation and Fractional Laplacian in the Case of Complex-Valued, Unbounded Variable Coefficient Wave Number μ
<p>We consider the Helmholtz equation and the fractional Laplacian in the case of the complex-valued unbounded variable coefficient wave number 𝜇, approximated by finite differences. In a recent analysis, singular value clustering and eigenvalue clustering have been proposed for a 𝜏 preconditioning when the variable coefficient wave number 𝜇 is uniformly bounded. Here, we extend the analysis to the unbounded case by focusing on the case of a power singularity. Several numerical experiments concerning the spectral behavior and convergence of the related preconditioned GMRES are presented.</p>