Related papers: The Integral Equation Method for a Steady Kinemati…
The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the…
Two different approaches to the Roberts dynamo problem are considered. Firstly, the equations governing the magnetic field are specified to both harmonic and subharmonic solutions and reduced to matrix eigenvalue problems, which are solved…
Some notable systems, such as room-temperature superconductors and materials for controlled nuclear fusion, require an accurate description of finite-temperature quantum matter. Stochastic path integral methods are finite-temperature and…
Numerical geodynamo simulations with parameters close to an Earth-like regime would be of great interest for understanding the dynamics of the Earth's liquid outer core and the associated geomagnetic field. Such simulations are far too…
Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial…
We analyze the convergence of the harmonic balance method for computing isolated periodic solutions of a large class of continuously differentiable Hilbert space valued differential-algebraic equations (DAEs). We establish asymptotic…
Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
A brief overview is given over recent results on the spectral properties of spherically symmetric MHD alpha2-dynamos. In particular, the spectra of sphere-confined fluid or plasma configurations with physically realistic boundary conditions…
Nonlinear eigenvalue equations arise naturally in quantum information theory, particularly in the variational quantification of entanglement. In this work, we present a hybrid analytical and numerical framework for evaluating the geometric…
We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution $\alpha<1$, and no external driving force is present, the energy of the…
Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the…
This paper deals with the numerical integration of Hamiltonian systems in which a stiff anharmonic potential causes highly oscillatory solution behavior with solution-dependent frequencies. The impulse method, which uses micro- and…
Regular convergence, together with various other types of convergence, has been studied since the 1970s for the discrete approximations of linear operators. In this paper, we consider the eigenvalue approximation of compact operators whose…
This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary…
The linear stability analysis of the Boltzmann kinetic equation has recently garnered research interest due to its potential applications in space exploration, where rarefaction effects can render the Navier Stokes equations invalid. Since…
Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems $Hv = \lambda v$, such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to…
In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The mathematical model we consider is based on the well-known…
Context. The recently developed test-field method permits to compute dynamo coefficients from global, direct numerical simulations. The subsequent use of these parameters in mean-field models enables us to compare self-consistent dynamo…
The hypothesis on complete integrability of equations describing the potential motion of incompressible ideal fluid with free surface in 2-D space in presence and absence of gravity was formulated by Dyachenko and Zakharov in 1994 [1].…