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The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
We investigate the modeling and simulation of ionic transport and charge conservation in lithium-ion batteries (LIBs) at the microscale. It is a multiphysics problem that involves a wide range of time scales. The associated computational…
The conductor-like polarization model (C-PCM) with switching/Gaussian smooth discretization is a widely used implicit solvation model in chemical simulations. However, its application in quantum mechanical calculations of large-scale…
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a…
The new class of alternating-conjugate splitting methods is presented and analyzed. They are obtained by concatenating a given composition involving complex coefficients with the same composition but with the complex conjugate coefficients.…
We carried out three-dimensional simulations, with about 1.4 million particles, of phase segregation in a low density binary fluid mixture, described mesoscopically by energy and momentum conserving Boltzmann-Vlasov equations. Using a…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
We consider a poromechanics model including frictionless contact mechanics. The resulting model consists of the Biot equations with contact boundary conditions leading to a variational inequality modelling mechanical deformations coupled to…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined in the unitary group. The schemes involve complex…
It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability…
The mean-field dynamics of a Bose-Einstein condensate is studied in presence of a microscopic trapping potential from which the condensate can escape via tunneling through finite barriers. We show that the method of complex scaling can be…
We present a circulant and skew-circulant splitting (CSCS) iterative method for solving large sparse continuous Sylvester equations $AX + XB = C$, where the coefficient matrices $A$ and $B$ are Toeplitz matrices. A theoretical study shows…
This paper is about partitioning in parallel and distributed simulation. That means decomposing the simulation model into a numberof components and to properly allocate them on the execution units. An adaptive solution based on…
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…
In this paper we consider various splitting schemes for unsteady problems containing the grad-div operator. The fully implicit discretization of such problems would yield at each time step a linear problem that couples all components of the…
Blind Compressed Sensing (BCS) is an extension of Compressed Sensing (CS) where the optimal sparsifying dictionary is assumed to be unknown and subject to estimation (in addition to the CS sparse coefficients). Since the emergence of BCS,…
Numerical models of weather and climate critically depend on long-term stability of integrators for systems of hyperbolic conservation laws. While such stability is often obtained from (physical or numerical) dissipation terms, physical…
The purpose of this paper is to study the existence and uniqueness of solutions to a system of Stochastic Differential Equations (SDEs). The coordinates are bounded by zero and one, and repulse each other according to a Coulombian like…
The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…