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Due to its significance in terms of wave phenomena a considerable effort has been put into the design of preconditioners for the Helmholtz equation. One option to derive a preconditioner is to apply a multigrid method on a shifted operator.…

We present a computational study of several preconditioning techniques for the GMRES algorithm applied to the stochastic diffusion equation with a lognormal coefficient discretized with the stochastic Galerkin method. The clear block…

Model-based iterative reconstruction plays a key role in solving inverse problems. However, the associated minimization problems are generally large-scale, nonsmooth, and sometimes even nonconvex, which present challenges in designing…

In recent years, dielectric rod based metasurface lenses have been particularly investigated for their potential applications in replacing the traditional bulky lens with high efficiency. However, the isolated granular structure may lead to…

We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial…

Finite element methods are effective for Helmholtz problems involving complex geometries and heterogeneous media. However, the resulting linear systems are often large, indefinite, and challenging for iterative solvers, particularly at high…

In this paper, we propose a deep-learning-based approach to a class of multiscale problems. THe Generalized Multiscale Finite Element Method (GMsFEM) has been proven successful as a model reduction technique of flow problems in…

An approximate formulation of a robust geometric program (RGP) as a convex program is proposed. Interest in using geometric programs (GPs) to model complex engineering systems has been growing, and this has motivated explicitly modeling the…

Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…

Sim-to-real transfer remains a significant challenge in soft robotics due to the unpredictability introduced by common manufacturing processes such as 3D printing and molding. These processes often result in deviations from simulated…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract stabilized framework, we prove that any mixed finite element…

Preconditioning is at the heart of iterative solutions of large, sparse linear systems of equations in scientific disciplines. Several algebraic approaches, which access no information beyond the matrix itself, are widely studied and used,…

We provide a functional view of distributional robustness motivated by robust statistics and functional analysis. This results in two practical computational approaches for approximate distributionally robust nonlinear optimization based on…

This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on applications in computational mechanics and design optimization. We leverage Mat\'ern-type…

In this paper we propose a method for the construction of locally conservative flux fields from Generalized Multiscale Finite Element Method (GMsFEM) pressure solutions. The flux values are obtained from an element-based postprocessing…

Standard Gaussian graphical models (GGMs) implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected form heterogeneous…

This work proposes a notion of robust reachability of one set from another set under constant control. This notion is used to construct a control strategy, involving sequential set-to-set reachability, which guarantees robust global…

In this paper we develop a class of efficient Galerkin boundary element methods for the solution of two-dimensional exterior single-scattering problems. Our approach is based upon construction of Galerkin approximation spaces confined to…

We prove that standard Gaussian random multipliers are expected to stabilize numerically both Gaussian elimination with no pivoting and block Gaussian elimination. Our tests show similar results where we applied circulant random multipliers…