Related papers: Extending fields in a level set method by solving …
This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. In this paper, we…
We discuss vertex patch smoothers as overlapping domain decomposition methods for fourth order elliptic partial differential equations. We show that they are numerically very efficient and yield high convergence rates. Furthermore, we…
We focus on a geometrical inverse problem that involves recovering discontinuities in electrical conductivity based on boundary measurements. This problem serves as a model to introduce a shape recovery technique that merges the…
This Paper conducts a thorough simulation study to assess the effectiveness of various acceleration techniques designed to enhance the conjugate gradient algorithm, which is used for solving large linear systems to accelerate Bayesian…
This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each…
The level set method is a widely used tool for solving reachability and invariance problems. However, some shortcomings, such as the difficulties of handling dissipation function and constructing terminal conditions for solving the…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
In this paper we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In the general case we have the solution as a multiresolution expansion in the base of…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…
High-order numerical methods for solving elliptic equations over arbitrary domains typically require specialized machinery, such as high-quality conforming grids for finite elements method, and quadrature rules for boundary integral…
The use of ensemble methods to solve inverse problems is attractive because it is a derivative-free methodology which is also well-adapted to parallelization. In its basic iterative form the method produces an ensemble of solutions which…
In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries…
Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…
A number of different multiscale methods have been developed as a robust alternative to upscaling and as a means for accelerated reservoir simulation of high-resolution geomodels. In their basic setup, multiscale methods use a restriction…
In this paper, we propose to use the eikonal equation as a boundary condition when advective or normal flow equations in the level set formulation are solved numerically on polyhedral meshes in the three-dimensional domain. Since the level…
For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
In this article, we apply the binary level set method to the Variational Implicit Solvent Model (VISM), which is a theoretical and computational tool to study biomolecular systems with complex topology. Central in VISM is an effective free…
This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or…