Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes

We present a new two-step "intermediate mortar" approach that efficiently extends the Mortar Element Method (MEM) to 3D meshes with nonconforming discretizations. The technique utilizes projection matrices derived in 2D, thereby avoiding the need to explicitly form large matrices for the 3D cases. The method also allows more flexibility for both h- and p-type adaptation. Parallel implementations with OpenMP and multithreading compiler directives are used to solve a moving heat source problem on SGI Origin and Cray MTA machines. Numerical results demonstrate the advantages of adaptive nonconforming meshes with MEM over uniformly fine meshes.