V.N.S.R. Dwarka
17 records found
1
Authored
We propose a matrix-free parallel two-level deflation method combined with the Complex Shifted Laplacian Preconditioner (CSLP) for two-dimensional heterogeneous Helmholtz problems encountered in seismic exploration, antennas, and medical imaging. These problems pose challenges ...
Iterative methods for time-harmonic waves
Towards accuracy and scalability
In recent years, domain decomposition based preconditioners have become popular tools to solve the Helmholtz equation. Notorious for causing a variety of convergence issues, the Helmholtz equation remains a challenging PDE to solve numerically. Even for simple model problems, ...
Pollution and accuracy of solutions of the Helmholtz equation
A novel perspective from the eigenvalues
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 research efforts aimed at iteratively solving the Helmholtz equation have focused on incorporating deation techniques for accelerating the convergence of Krylov subpsace methods. The requisite for these efforts lies in the fact that the widely used and well-acknowledged ...