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—Mantle convection is the principal control on the thermal and geological evolution of the Earth. Mantle convection modeling involves solution of the mass, momentum , and energy equations for a viscous, creeping, incom-pressible non-Newtonian fluid at high Rayleigh and Peclet numbers. Our goal is to conduct global mantle convection simulations that can(More)
We present scalable algorithms for parallel adaptive mesh refinement and coarsening (AMR), partitioning, and 2:1 balancing on computational domains composed of multiple connected 2D quadtrees or 3D octrees, referred to as a forest of octrees. By distributing the union of octants from all octrees in parallel, we combine the high scalability proven previously(More)
Today's largest supercomputers have 100,000s of processor cores and offer the potential to solve partial differential equations discretized by billions of unknowns. However, the complexity of scaling to such large machines and problem sizes has so far prevented the emergence of generic software libraries that support such computations, although these would(More)
Many problems are characterized by dynamics occurring on a wide range of length and time scales. One approach to overcoming the tyranny of scales is adaptive mesh refinement/coarsening (AMR), which dynamically adapts the mesh to resolve features of interest. However, the benefits of AMR are difficult to achieve in practice, particularly on the petascale(More)
We address the solution of large-scale statistical inverse problems in the framework of Bayesian inference. The Markov chain Monte Carlo (MCMC) method is the most popular approach for sampling the posterior probability distribution that describes the solution of the statistical inverse problem. MCMC methods face two central difficulties when applied to(More)
Plate tectonics is regulated by driving and resisting forces concentrated at plate boundaries, but observationally constrained high-resolution models of global mantle flow remain a computational challenge. We capitalized on advances in adaptive mesh refinement algorithms on parallel computers to simulate global mantle flow by incorporating plate motions,(More)
A new generation, parallel adaptive-mesh mantle convection code, Rhea, is described and benchmarked. Rhea targets large-scale mantle convection simulations on parallel computers, and thus has been developed with a strong focus on computational efficiency and parallel scala-bility of both mesh handling and numerical solvers. Rhea builds mantle convection(More)
We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the(More)
We present applications of a cellular automaton approach to pedestrian dynamics introduced in [1, 2]. It is shown that the model is able to reproduce collective effects and self-organization phenomena encountered in pedestrian traffic, e.g. lane formation in counterflow through a large corridor and oscillations at doors. Furthermore we present simple(More)