Related papers: Tensor calculus in spherical coordinates using Jac…
A three-dimensional finite-difference solver has been developed and implemented for Boussinesq convection in a spherical shell. The solver transforms any complex curvilinear domain into an equivalent Cartesian domain using Jacobi…
A comprehensive algebro-geometric integration of the two component Nonlinear Vector Schr\"odinger equation (Manakov system) is developed. The allied spectral variety is a trigonal Riemann surface, which is described explicitly and the…
An effective numerical method is presented for optimizing model parameters that can be applied to any type of system of non-linear equations and any number of data-points, which does not require explicit formulation of the objective…
A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as…
The computational cost associated with reducing tensor integrals to scalar integrals using the Passarino-Veltman method is dominated by the diagonalisation of large systems of equations. These systems of equations are sized according to the…
We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…
We consider the problem of estimating a rank-one nonsymmetric matrix under additive white Gaussian noise. The matrix to estimate can be written as the outer product of two vectors and we look at the special case in which both vectors are…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
The generalized Jacobi equation is a differential equation in local coordinates that describes the behavior of infinitesimally close geodesics with an arbitrary relative velocity. In this note we study some transformation properties for…
In this paper, we consider a family of Jacobi-type algorithms for simultaneous orthogonal diagonalization problem of symmetric tensors. For the Jacobi-based algorithm of [SIAM J. Matrix Anal. Appl., 2(34):651--672, 2013], we prove its…
The spectral decomposition of a symmetric, second-order tensor is widely adopted in many fields of Computational Mechanics. As an example, in elasto-plasticity under large strain and rotations, given the Cauchy deformation tensor, it is a…
Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention…
We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable…
A partial-wave method is developed to deal with small molecules dominated by a central atom as an extension of earlier single-center methods. In particular, a model potential for the water molecule is expanded over a basis of spherical…
We study the Dirac equation in 3+1 dimensions with a general combination of scalar, vector and tensor interactions with arbitrary strengths, all of them described by central Coulomb potentials acting on a particular plane of motion. For the…
In the present paper we use twistor theory in order to solve two problems related to harmonic maps from surfaces to Euclidean spheres $\mathbb{S}^n$. First, we propose a new approach to isoperimetric inequalities based on energy index.…
A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through…
We numerically examine the exterior solution of spherically symmetric and static configuration in scalar-tensor theories by using the nonminimally coupled scalar field with zero potential as our sample model. Our main purpose in this work…
In quantum theory, the so-called "spinless Salpeter equation," the relativistic generalization of the nonrelativistic Schroedinger equation, is used to describe both bound states of scalar particles and the spin-averaged spectra of bound…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…