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A discretization method with non-matching grids is proposed for the coupled Stokes-Darcy problem that uses a mortar variable at the interface to couple the marker and cell (MAC) method in the Stokes domain with the Raviart-Thomas mixed…
Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes-Darcy model with Beaver-Joseph-Saffman interface condition in literatures, the numerical analysis only get…
In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of…
We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain…
We consider the problem of jointly modeling and clustering populations of tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. To effectively tackle the high dimensionality of tensor objects, we…
Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value…
We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…
The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…
Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate…
In this paper, we propose a new numerical scheme for the coupled Stokes-Darcy model with Beavers-Joseph-Saffman interface condition. We use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…
This work focuses on the development and analysis of a partitioned numerical method for moving domain, fluid-structure interaction problems. We model the fluid using incompressible Navier-Stokes equations, and the structure using linear…
Bayesian inverse problems are often computationally challenging when the forward model is governed by complex partial differential equations (PDEs). This is typically caused by expensive forward model evaluations and high-dimensional…
As deep learning-based computer vision algorithms continue to advance the state of the art, their robustness to real-world data continues to be an issue, making it difficult to bring an algorithm from the lab to the real world.…
The aim of this paper is to propose a systematic way to obtain convergent finite element schemes for the Darcy-Stokes flow problem by combining well-known mixed finite elements that are separately convergent for Darcy and Stokes problems.…
In this paper we present a new algorithm for the solution of Hamilton-Jacobi-Bellman equations related to optimal control problems. The key idea is to divide the domain of computation into subdomains which are shaped by the optimal dynamics…
This paper derives optimal coefficients for optimized Schwarz iterations for the time-dependent Stokes-Darcy problem using an innovative strategy to solve a nonstandard min-max problem. The coefficients take into account both physical and…
This paper presents a pressure-robust discretizations, specifically within the context of optimal control problems for the Stokes-Darcy system. The study meticulously revisits the formulation of the divergence constraint and the enforcement…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…