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p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
We present scalable algorithms for parallel adaptive mesh refinement and coarsening (AMR), partitioning, and 2:1 balancing on computational domains composed of multiple connected two-dimensional…
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A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
TLDR
This work addresses the solution of large-scale statistical inverse problems in the framework of Bayesian inference with a so-called Stochastic Monte Carlo method.
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A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion
TLDR
A computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems that incorporates algorithms for manipulating the prior, constructing a low rank approximation of the data-informed component of the posterior covariance operator, and exploring the posterior that together ensure scalability of the entire framework to very high parameter dimensions.
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Extreme-scale UQ for Bayesian inverse problems governed by PDEs
TLDR
This work addresses uncertainty quantification for large-scale inverse problems in a Bayesian inference framework by exploiting the fact that the data are typically informative about low-dimensional manifolds of parameter space to construct low rank approximations of the covariance matrix of the posterior pdf via a matrix-free randomized method.
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Multi‐scale dynamics and rheology of mantle flow with plates
Fundamental issues in our understanding of plate and mantle dynamics remain unresolved, including the rheology and state of stress of plates and slabs; the coupling between plates, slabs and mantle;…
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The Dynamics of Plate Tectonics and Mantle Flow: From Local to Global Scales
TLDR
Computational advances enable the modeling of global geophysical processes to the scale of a kilometer and reveal unexpected insights into localized processes, such as subduction zone mechanics, thermal anomalies in the lower mantle, and the speed of movement of oceanic plates.
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Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space
TLDR
A model-constrained adaptive sampling methodology is proposed for the reduction of large-scale systems with high-dimensional parametric input spaces using an efficient adaptive algorithm that scales well to systems with a large number of parameters.
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A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media
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Scalable Parallel Octree Meshing for TeraScale Applications
TLDR
Octor provides a novel data access interface to parallel PDE solvers and parallel visualization pipelines, making it possible to develop tightly coupled end-to-end finite element simulations on terascale systems.
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Non‐linear model reduction for uncertainty quantification in large‐scale inverse problems
TLDR
A model reduction approach to the solution of large‐scale statistical inverse problems in a Bayesian inference setting that employs masked projection of the discrete equations and shows similarities among the existing techniques of gappy proper orthogonal decomposition, missing point estimation, and empirical interpolation via coefficient‐function approximation.
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