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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 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)
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)
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)
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)
We present a parallel multigrid method for solving variable-coefficient elliptic partial differential equations on arbitrary geometries using highly adapted meshes. Our method is designed for meshes that are built from an unstructured hexahedral macro mesh, in which each macro element is adaptively refined as an octree. This forest-of-octrees approach(More)
Adaptive mesh refinement and coarsening (AMR) is essential for the numerical solution of partial differential equations (PDEs) that exhibit behavior over a wide range of length and time scales. Because of the complex dynamic data structures and communication patterns and frequent data exchange and redistribution, scaling dynamic AMR to tens of thousands of(More)
Quantifying uncertainties in large-scale simulations has emerged as the central challenge facing CS&E. When the simulations require supercomputers, and uncertain parameter dimensions are large, conventional UQ methods fail. Here we address uncertainty quantification for large-scale inverse problems in a Bayesian inference framework: given data and model(More)