The penalty boundary method for solving boundary value problems with finite elements

Finite element analysis (FEA) has become a popular tool for solving boundary value problems in engineering design. The ability of FEA to solve problems involving complex geometry by subdividing the domain into smaller, simpler domains theoretically allows the designer to solve problems of any geometric complexity. However, discretization of the geometry can prove very complex, leading to meshes with poor quality and error in the FEA solution. Traditional methods for applying boundary conditions in FEA require the mesh to conform to the geometry boundaries. This in turn requires complex meshing algorithms for automated mesh generation from CAD geometry, particularly when using quadrilateral and hexahedral elements. The penalty boundary method (PBM) is presented as a method that significantly reduces the time required generating finite element models because the mesh is not required to conform to the CAD geometry. The PBM employs penalty methods to apply boundary conditions on a simple, regular mesh that is not required to coincide with the boundaries of the problem domain. As a result, mesh generation is greatly simplified and error associated with poor mesh duality in traditional finite element meshes is avoided