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Abstract: In this paper, we present a parallel Image-to-Mesh Conversion (I2M) algorithm with quality and fidelity guarantees achieved by dynamic point insertions and removals. Starting directly from an image, its implementation is capable of recovering the isosurface and meshing the volume with tetrahedra of good shape. Our tightly-coupled shared-memory parallel speculative execution paradigm employs carefully designed contention managers, load balancing, synchronization and optimizations schemes. These techniques are shown to boost not only the parallel but also the single-threaded efficiency of our code. Specifically, our single-threaded performance is faster than both CGAL and TetGen, the state of the art sequential open source meshing tools we are aware of. The effectiveness of our method is demonstrated on Blacklight, the Pittsburgh Supercomputing Center’s cache-coherent NUMA machine. We observe a more than 82% strong scaling efficiency for up to 64 cores, and a more than 82% weak scaling efficiency for up to 144 cores, reaching a rate of more than 14.3 million elements per second. This is the fastest 3D Delaunay mesh generation and refinement algorithm, to the best of our knowledge. [Copyright &y& Elsevier]

Abstract: In this paper we present a new parallel multi-frontal direct solver, dedicated for the hp Finite Element Method (hp-FEM). The self-adaptive hp-FEM generates in a fully automatic mode, a sequence of hp-meshes delivering exponential convergence of the error with respect to the number of degrees of freedom (d.o.f.) as well as the CPU time, by performing a sequence of hp refinements starting from an arbitrary initial mesh. The solver constructs an initial elimination tree for an arbitrary initial mesh, and expands the elimination tree each time the mesh is refined. This allows us to keep track of the order of elimination for the solver. The solver also minimizes the memory usage, by de-allocating partial LU factorizations computed during the elimination stage of the solver, and recomputes them for the backward substitution stage, by utilizing only about 10% of the computational time necessary for the original computations. The solver has been tested on 3D Direct Current (DC) borehole resistivity measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive -FEM, with finite elements of various sizes and polynomial orders of approximation varying from to . From the presented experiments it follows that the parallel solver scales well up to the maximum number of utilized processors. The limit for the solver scalability is the maximum sequential part of the algorithm: the computations of the partial LU factorizations over the longest path, coming from the root of the elimination tree down to the deepest leaf. [Copyright &y& Elsevier]