相关论文: A boundary integral equation approach to computing…
This paper proposes a new boundary integral equation (BIE) methodology based on the perfectly matched layer (PML) truncation technique for solving the electromagnetic scattering problems in a multi-layered medium. Instead of using the…
We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on…
This paper presents eigensolution and non-modal analyses for immersed boundary methods (IBMs) based on volume penalization for the linear advection equation. This approach is used to analyze the behavior of flux reconstruction (FR)…
The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by…
We propose a method combining boundary integral equations and neural networks (BINet) to solve partial differential equations (PDEs) in both bounded and unbounded domains. Unlike existing solutions that directly operate over original PDEs,…
In this paper we propose and analyze spectral-Galerkin methods for the Stokes eigenvalue problem based on the stream function formulation in polar geometries. We first analyze the stream function} formulated fourth-order equation under the…
We develop a Bayesian methodology for numerical solution of the incompressible Navier--Stokes equations with quantified uncertainty. The central idea is to treat discretized Navier--Stokes dynamics as a state-space model and to view…
We study Sturm--Liouville differential operators on the time scales consisting of a finite number of isolated points and segments. In a previous paper it was established that such operators are uniquely determined by their spectral…
We develop a mathematically and physically sound definition of the spectrally-hyperviscous Navier-Stokes equations (SHNSE) on general bounded domains \Omega with zero (no-slip) boundary conditions prescribed on \varGamma=\partial\varOmega.…
We study the Stokes--Poisson--Boltzmann equations with Dirichlet and Navier boundary conditions. The system consists of the incompressible Stokes equations coupled with a nonlinear Poisson--Boltzmann equation through electrostatic forcing…
We address Euler's equations for irrotational gravity waves in an infinitely deep fluid rewritten in conformal variables. Stokes waves are traveling waves with the smooth periodic profile. In agreement with the previous numerical results,…
The purpose of this paper is to investigate some spectral properties of Sturm-Liouville type problems with interior singularities. Some of the mathematical aspects necessary for developing own technique presented. By applying this technique…
This paper describes the recently developed mixed mimetic spectral element method for the Stokes problem in the vorticity-velocity-pressure formulation. This compatible discretization method relies on the construction of a conforming…
We theoretically investigate polarization properties of a two-component Bose-Einstein condensate (BEC) and influence of decoherence induced by environment on BEC polarization through introducing four BEC Stokes operators which are quantum…
We consider an initial-boundary value problem for the 4D Navier-Stokes equations posed on bounded smooth domains. We prove the existence and uniqiueness of regular solutions as well as their exponential decay and additional regularity…
The aim of this work is to point out that the class of free boundary problems governed by second order autonomous ordinary differential equations can be transformed to initial value problems. Interest in the numerical solution of free…
The boundary integral equation method ascertains explicit relations between localized surface phonon and plasmon polariton resonances and the eigenvalues of its associated electrostatic operator. We show that group-theoretical analysis of…
We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields. The spectral problem for this model can be formulated in terms of functional equations obtained by separation of…
This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…
In this paper, we construct growing modes of the linearized Navier-Stokes equations about generic stationary shear flows of the boundary layer type in a regime of sufficiently large Reynolds number: $R \to \infty$. Notably, the shear…