hIPPYlib: An extensible software framework for large-scale inverse problems governed by PDEs: Part I: Deterministic inversion and linearized Bayesian inference
We present an extensible software framework, hIPPYlib, for solution of large-scale
deterministic and Bayesian inverse problems governed by partial differential equations …
deterministic and Bayesian inverse problems governed by partial differential equations …
High-performance finite elements with MFEM
The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for
finite element discretizations. MFEM supports numerous types of finite element methods and …
finite element discretizations. MFEM supports numerous types of finite element methods and …
Multi-output multilevel best linear unbiased estimators via semidefinite programming
Multifidelity forward uncertainty quantification (UQ) problems often involve multiple
quantities of interest and heterogeneous models (eg, different grids, equations, dimensions …
quantities of interest and heterogeneous models (eg, different grids, equations, dimensions …
Spatial modeling algorithms for reactions and transport in biological cells
Biological cells rely on precise spatiotemporal coordination of biochemical reactions to
control their functions. Such cell signaling networks have been a common focus for …
control their functions. Such cell signaling networks have been a common focus for …
Uncertainty quantification of parenchymal tracer distribution using random diffusion and convective velocity fields
Background Influx and clearance of substances in the brain parenchyma occur by a
combination of diffusion and convection, but the relative importance of these mechanisms is …
combination of diffusion and convection, but the relative importance of these mechanisms is …
Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization
This work highlights an approach for incorporating realistic uncertainties into scientific
computing workflows based on finite elements, focusing on prevalent applications in …
computing workflows based on finite elements, focusing on prevalent applications in …
Analysis of boundary effects on PDE-based sampling of Whittle--Matérn random fields
We consider the generation of samples of a mean-zero Gaussian random field with Matérn
covariance function. Every sample requires the solution of a differential equation with …
covariance function. Every sample requires the solution of a differential equation with …
Optimal sensor and actuator placement for feedback control of vortex shedding
We consider linear feedback control of the two-dimensional flow past a cylinder at low
Reynolds numbers, with a particular focus on the optimal placement of a single sensor and a …
Reynolds numbers, with a particular focus on the optimal placement of a single sensor and a …
Multilevel approximation of Gaussian random fields: fast simulation
We propose and analyze several multilevel algorithms for the fast simulation of possibly
nonstationary Gaussian random fields (GRFs) indexed, for example, by the closure of a …
nonstationary Gaussian random fields (GRFs) indexed, for example, by the closure of a …
A probabilistic finite element method based on random meshes: A posteriori error estimators and Bayesian inverse problems
A Abdulle, G Garegnani - Computer Methods in Applied Mechanics and …, 2021 - Elsevier
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty
quantification of elliptic partial differential equations based on random meshes, which we …
quantification of elliptic partial differential equations based on random meshes, which we …