Related papers: Preconditioning across parameter space for the par…
Uncertainty in physical parameters can make the solution of forward or inverse light scattering problems in astrophysical, biological, and atmospheric sensing applications, cost prohibitive for real-time applications. For example, given a…
In this paper we consider a class of robust multilevel precontioners for the Helmholtz equation with high wave number. The key idea in this work is to use the continuous interior penalty finite element methods (CIP-FEM) studied in…
We establish a new iterative method for solving a class of large and sparse linear systems of equations with three-by-three block coefficient matrices having saddle point structure. Convergence properties of the proposed method are studied…
In various fields, statistical models of interest are analytically intractable. As a result, statistical inference is greatly hampered by computational constraints. However, given a model, different users with different data are likely to…
In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to…
In this paper, an efficient solver for the Helmholtz equation using a noval approximation space is developed. The ingradients of the method include the approximation space recently proposed, a discontinuous Galerkin scheme extensively used,…
We present MMbeddings, a probabilistic embedding approach that reinterprets categorical embeddings through the lens of nonlinear mixed models, effectively bridging classical statistical theory with modern deep learning. By treating…
This work considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…
Deterministic neural operators perform well on many PDEs but can struggle with the approximation of high-frequency wave phenomena, where strong input-to-output sensitivity makes operator learning challenging, and spectral bias blurs…
We consider wave scattering from a system of highly contrasting resonators with time-modulated material parameters. In this setting, the wave equation reduces to a system of coupled Helmholtz equations that models the scattering problem. We…
Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an…
The Helmholtz equation is related to seismic exploration, sonar, antennas, and medical imaging applications. It is one of the most challenging problems to solve in terms of accuracy and convergence due to the scalability issues of the…
In this paper, we focus on a new wave equation described wave propagation in the attenuation medium. In the first part of this paper, based on the time-domain space fractional wave equation, we formulate the frequency-domain equation named…
Preconditioning of a linear system obtained from spectral discretization of time-dependent PDEs often results in a full matrix which is expensive to compute and store specially when the problem size increases. A matrix-free implementation…
We consider the identification of spatially distributed parameters under $H^1$ regularization. Solving the associated minimization problem by Gauss-Newton iteration results in linearized problems to be solved in each step that can be cast…
This manuscript presents an efficient solver for the linear system that arises from the Hierarchical Poincar\'e-Steklov (HPS) discretization of three dimensional variable coefficient Helmholtz problems. Previous work on the HPS method has…
This paper details how to parameterize the posterior distribution of state-space systems to generate improved optimization problems for system identification using variational inference. Three different parameterizations of the assumed…
Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…
We present a two-level preconditioner for solving linear systems arising from the discretization of the elliptic, linear-elastic deformation equation, in displacement unknowns, over domains that have arbitrary geometric and topological…
We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…