Pollution and accuracy of solutions of the Helmholtz equation: A novel perspective from the eigenvalues

In researching the Helmholtz equation, the focus has either been on the accuracy of the numerical solution (pollution) or the acceleration of the convergence of a preconditioned Krylov-based solver (scalability). While it is widely recognized that the convergence properties can be investigated by studying the eigenvalues, information from the...

Towards accuracy and scalability: Combining Isogeometric Analysis with deflation to obtain scalable convergence for the Helmholtz equation

Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical wave number k) requires the mesh resolution to be kept fine enough to obtain accurate solutions. A recent study showed that the use of Isogeometric Analysis (IgA)...