Related papers: Decreasing Minimization on Base-Polyhedra: Relatio…
We give a deterministic polynomial time $2^{O(r)}$-approximation algorithm for the number of bases of a given matroid of rank $r$ and the number of common bases of any two matroids of rank $r$. To the best of our knowledge, this is the…
The discretization of elliptic PDEs leads to large coupled systems of equations. Domain decomposition methods (DDMs) are one approach to the solution of these systems, and can split the problem in a way that allows for parallel computing.…
We present an algebraic method for constructing a highly effective coarse grid correction to accelerate domain decomposition. The coarse problem is constructed from the original matrix and a small set of input vectors that span a low-degree…
We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…
We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a…
Computing the core decomposition of a graph is a fundamental problem that has recently been studied in the differentially private setting, motivated by practical applications in data mining. In particular, Dhulipala et al. [FOCS 2022] gave…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
In this paper, the authors devise a new discretization scheme for div-curl systems defined in connected domains with heterogeneous media by using the weak Galerkin finite element method. Two types of boundary value problems are considered…
We introduce DDE-Solver, a Maple package designed for solving Discrete Differential Equations (DDEs). These equations are functional equations relating algebraically a formal power series F(t, u) with polynomial coefficients in a…
This paper is concerned with approximations and related discretization error estimates for the normal derivatives of solutions of linear elliptic partial differential equations. In order to illustrate the ideas, we consider the Poisson…
Base polytopes of polymatroids, also known as generalized permutohedra, are polytopes whose edges are parallel to a vector of the form $\mathbf{e}_i - \mathbf{e}_j$. We consider the following computational problem: Given two vertices of a…
Steady and unsteady Poisson and Stokes equations are solved using mesh dependent Finite Element Method and meshless Radial Basis Function Collocation Method to compare the performances of these two numerical techniques across several…
We consider standard tracking-type, distributed elliptic optimal control problems with $L^2$ regularization, and their finite element discretization. We are investigating the $L^2$ error between the finite element approximation $u_{\varrho…
This paper presents a PDE-based approach to finding an optimal canonical basis with which to represent a nearly integrable Hamiltonian. The idea behind the method is to continuously deform the initial canonical basis in such a way that the…
We address the optimal control problems arising from partial differential equations with large discrete dimensional control systems. To obtain reduced order models, we find basis elements from the canonical polyadic (CP) decomposition.…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…
We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…
This paper considers a large class of linear operator equations, including linear boundary value problems for partial differential equations, and treats them as linear recovery problems for objects from their data. Well-posedness of the…
We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the…