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We propose and analyze a perturbative regularization method to approximate quadratic optimization problems with finite-dimensional degeneracy. The original problem is first approximated by a regularized problem depending on a small positive…
We present a new method for solving symbolically zero--dimensional polynomial equation systems in the affine and toric case. The main feature of our method is the use of problem adapted data structures: arithmetic networks and…
Mathematical Program with Complementarity Constraints (MPCC) plays a very important role in many fields such as engineering design, economic equilibrium, multilevel game, and mathematical programming theory itself. In theory its constraints…
We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems…
The Satisfiability Modulo Theories (SMT) issue concerns the satisfiability of formulae from multiple background theories, usually expressed in the language of first-order predicate logic with equality. SMT solvers are often based on…
In this paper, we introduce MPM Lite, a new hybrid Lagrangian/Eulerian method that eliminates the need for particle-based quadrature at solve time. Standard MPM practices suffer from a performance bottleneck where expensive implicit solves…
We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the equations under study, as well as that…
This paper presents a novel parallel splitting algorithm for solving quasi-static multiple-network poroelasticity (MPET) equations. By introducing a total pressure variable, the MPET system can be reformulated into a coupled…
A new approach to the solution of boundary value problems within the so-called fictitious domain methods philosophy is proposed which avoids well known shortcomings of other fictitious domain methods, including the need to generate…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
We propose a feasible active set method for convex quadratic programming problems with non-negativity constraints. This method is specifically designed to be embedded into a branch-and-bound algorithm for convex quadratic mixed integer…
High-order methods gain more and more attention in computational fluid dynamics. However, the potential advantage of these methods depends critically on the availability of efficient elliptic solvers. With spectral-element methods, static…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space-time by means of a generalized microcanonical ensemble similar to the one of the standard…
We develop a decomposition method based on the augmented Lagrangian framework to solve a broad family of semidefinite programming problems, possibly with nonlinear objective functions, nonsmooth regularization, and general linear…
In this short note, we present a new technique to accelerate the convergence of a FFT-based solver for numerical homogenization of complex periodic media proposed by Moulinec and Suquet in 1994. The approach proceeds from discretization of…
We investigate a modified split-step Fourier method (SSFM) by including low-pass filters in the linear steps. This method can simultaneously achieve a higher simulation accuracy and a slightly reduced complexity.
The method of fundamental solutions (MFS) is a numerical method for solving boundary value problems involving linear partial differential equations. It is well known that it can be very effective assuming regularity of the domain and…
Quantum computing promises transformative impacts in simulating Hamiltonian dynamics, essential for studying physical systems inaccessible by classical computing. However, existing compilation techniques for Hamiltonian simulation, in…
We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular…
In this paper, we first introduce the reader to the Basic Scheme of Moulinec and Suquet in the setting of quasi-static linear elasticity, which takes advantage of the fast Fourier transform on homogenized microstructures to accelerate…