mbem

mbemmollified boundary element method

mbem is a boundary element method for 3-D linear elasticity built on mollified Green's functions. Following Cortez, the point force is replaced by a smooth blob of width ε and the elastostatic equations are then solved exactly — so the kernels are singular nowhere and still satisfy a PDE, which softening the kernel by hand would not. A fault therefore has a finite width ε, and stress is defined on the fault itself, where classical dislocation theory returns a value that ordinary integration does not define. Each triangle's contribution is integrated in closed form, which decouples ε from the mesh size h.

Paper: Meade, B. J. (2026), Three dimensional non-singular mollified elastic dislocation theory for extended width fault zones and inhomogeneous boundary element models, arXiv:2609.15601. arxiv.org/abs/2609.15601

Code: github.com/brendanjmeade/mbem

Developed by Brendan Meade and Claude.

Elastic maximum shear stress through a 400 × 400 × 200 km box, from a stored solve — 24,348 unknowns, read out on a 79,000-point grid. The box holds a surface-breaking strike-slip fault (pink), a cylindrical inclusion ten times softer than its host (blue), and a 2 km Gaussian hill on the free surface, which the fault mesh is warped to follow. Drag to orbit. The eigenstress of every mollified jump has been subtracted, so this is the elastic stress, and every element is shown. See Concepts for what that means and Examples to move the slices yourself.