BEM and FEM: A Comparison
All our software programs incorporate a Finite Element Method (FEM) solver along with a Boundary Element Method (BEM) solver. FEM is a common powerful numerical method for solution of partial differential equations in applications which need to capture local effects. For a given design, the FEM requires the entire geometry, including the surrounding region, to be modeled with finite elements. A system of linear equations is generated to calculate the potential (scalar or vector) at the nodes of each element.
For some problems, however, an alternate boundary-element formulation can be much more efficient. BEM is the method of choice for applications requiring analysis of space around a device, and the exact modeling of boundaries. BEM uses an integral formulation of Maxwell’s Equations, which allows for very accurate field calculations. Unlike FEM the electric and magnetic fields are computed directly from the source. This technique produces accuracies not attainable by Finite Element Method. Therefore, the basic difference between these two techniques is the fact that BEM only needs to solve for unknowns on the boundaries, whereas FEM solves for unknowns in the volume. Thanks to BEM, only active regions require discretization, allowing fields to be calculated anywhere in the “world”. The combination of these two solvers offers exceptional facility in the analysis of electromagnetic problems.