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Computing accurate splines of degree greater than three is still a challenging task in today's applications. In this type of interpolation, high-order derivatives are needed on the given mesh. As these derivatives are rarely known and are…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
We study the Boltzmann equation in a smooth bounded domain featuring a mixed boundary condition. Specifically, gas particles experience specular reflection in two parallel plates, while diffusive reflection occurs in the remaining portion…
Periodic boundary conditions are commonly applied in molecular dynamics simulations in the microcanonical (NVE), canonical (NVT) and isothermal-isobaric (NpT) ensembles. In their simplest application, a biological system of interest is…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
In this paper, we propose two approaches to apply boundary conditions for bond-based peridynamic models. There has been in recent years a renewed interest in the class of so-called non-local models, which include peridynamic models, for the…
We study the Hubbard and Heisenberg models on hyperbolic lattices with open boundary conditions by means of mean-field approximations, spin-wave theory, and quantum Monte Carlo (QMC) simulations. For the Hubbard model we use the…
Recent developments in multiscale computation allow the solution of ``coarse equations'' for the expected macroscopic behavior of microscopically/stochastically evolving particle distributions without ever obtaining these coarse equations…
We study multiscale scattered data interpolation schemes for globally supported radial basis functions with focus on the Mat\'ern class. The multiscale approximation is constructed through a sequence of residual corrections, where radial…
This paper addresses the well posedness of a dynamical model of perfect plasticity with mixed boundary conditions for general closed and convex elasticity sets. The proof relies on an asymptotic analysis of the solution of a perfect…
We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We announce…
The totally asymmetric simple exclusion process with generalized update is a version of the discrete time totally asymmetric exclusion process with an additional inter-particle interaction that controls the degree of particle clustering.…
We introduce a neural-preconditioned iterative solver for Poisson equations with mixed boundary conditions. Typical Poisson discretizations yield large, ill-conditioned linear systems. Iterative solvers can be effective for these problems,…
In this paper, we extend the Generalized Finite Difference Method (GFDM) on unknown compact submanifolds of the Euclidean domain, identified by randomly sampled data that (almost surely) lie on the interior of the manifolds. Theoretically,…
Modeling the chemical, electric, and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic device setting involves the solution of partial differential…
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat…
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be…
Unfitted boundary methods are widely used to numerically solve partial differential equations (PDEs) on irregular domains, avoiding the computational burden of generating boundary-conforming grids. In the finite-difference framework,…
We describe a three-stage procedure to analyze the dependence of Poisson Boltzmann calculations on the shape, size and geometry of the boundary between solute and solvent. Our study is carried out within the boundary element formalism, but…
Previous studies on computational modeling of tooth movement in orthodontic treatments are limited to a single model and fail in generalizing the simulation results to other patients. To this end, we consider multiple patients and focus on…