New Laplace and Helmholtz solvers
Provides faster and more accurate solvers for PDE problems on domains with corners, a known bottleneck in computational science.
New rational-function-based algorithms solve Laplace and Helmholtz problems on 2D domains with corners faster and more accurately than finite elements and integral equations, challenging existing numerical analysis assumptions.
New numerical algorithms based on rational functions are introduced that can solve certain Laplace and Helmholtz problems on two-dimensional domains with corners faster and more accurately than the standard methods of finite elements and integral equations. The new algorithms point to a reconsideration of the assumptions underlying existing numerical analysis for partial differential equations.