Related papers: An Equation-By-Equation Method for Solving the Mul…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
Researchers in physical science aim to uncover universal features in strongly interacting many-body systems, often hidden in complicated observables like entanglement entropy (EE). The non-local nature of EE makes it challenging to compute…
We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time discretizations and investigate the influence of iterative methods used to solve the arising nonlinear equations. We show…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
In this paper, an efficient and accurate unified approach is proposed to solve transverse magnetic scattering problems by multilayer embedded objects. In the proposed approach, an equivalent current density is derived when the equivalent…
Strongly coupled immersed boundary (IB) methods solve the nonlinear fluid and structural equations of motion simultaneously for strongly enforcing the no-slip constraint on the body. Handling this constraint requires solving several large…
The homogeneous isotropic Boltzmann equation (HIBE) is a fundamental dynamic model for many applications in thermodynamics, econophysics and sociodynamics. Despite recent hardware improvements, the solution of the Boltzmann equation remains…
Damping of structures and systems is often dominated by frictional dissipation in connections, the prediction of which remains a longstanding scientific challenge. Previous studies have shown that the actual topography of contact interfaces…
Extended Thermodynamics is the natural framework in which to study the physics of fluids, because it leads to symmetric hyperbolic systems of field laws, thus assuming important properties such as finite propagation speeds of shock waves…
We propose a novel method for the efficient and accurate iterative solution of frequency domain integral equations (IEs) that are used for large/multi-scale electromagnetic scattering problems. The proposed method uses a novel…
We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the…
We derive the porous medium equation from an interacting particle system which belongs to the family of exclusion processes, with nearest neighbor exchanges. The particles follow a degenerate dynamics, in the sense that the jump rates can…
We establish Extended Thermodynamics (ET) of rarefied polyatomic gases with six independent fields, i.e., the mass density, the velocity, the temperature and the dynamic pressure, without adopting the near-equilibrium approximation. The…
This paper presents a new boundary integral equation (BIE) method for simulating particulate and multiphase flows through periodic channels of arbitrary smooth shape in two dimensions. The authors consider a particular system---multiple…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
We establish the existence and compactness of global martingale entropy solutions with finite relative-energy for the stochastically forced system of isentropic Euler equations governed by a general pressure law. To achieve these, a…
The Poisson-Boltzmann equation (PBE) is an implicit solvent continuum model for calculating the electrostatic potential and energies of ionic solvated biomolecules. However, its numerical solution remains a significant challenge due strong…
We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an…
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and…
The Maximum Entropy Method (MEM) is a popular data analysis technique based on Bayesian inference, which has found various applications in the research literature. While the MEM itself is well-grounded in statistics, I argue that its…