Discrete Differential Forms for the Numerical Solution of Helmholtz Equations

摘要

Partial differential equations that arise in computational electromagnetics and acoustics can be written with the common operators grad, div and curl. However the methodology of differential forms allows to formulate the partial differential equations in a compact and elegant way. It is also shown that the common procedure of Galerkin discretization can also be applied to that new formulations. Furthermore the implementation should also follow that concept to mimic the behaviour and properties of differential forms. Examples prove the validity of the implementation by using the method of manufactured solutions.