Related papers: String kernel representations in elastostatics
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…
We present a family of Virtual Element Methods for three-dimensional linear elasticity problems based on the Hellinger-Reissner variational principle. A convergence and stability analysis is developed. Moreover, using the hybridization…
Many problems of applied mathematics are reduced to the solution of integral equations with special functions in kernels, therefore the inversion formulas for such equations play an important role in solving boundary value problems for…
We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment…
This paper introduces a novel statistical regression framework that allows the incorporation of consistency constraints. A linear and nonlinear (kernel-based) formulation are introduced, and both imply closed-form analytical solutions. The…
We consider the problems of the numerical solution of the Cauchy problem for an evolutionary equation with memory when the kernel of the integral term is a difference one. The computational implementation is associated with the need to work…
Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic…
We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin…
In this paper we derive some new invariant solutions of Einstein-Maxwell's field equations for string fluid as source of matter in cylindrically symmetric space-time with Variable Magnetic Permeability. We also discuss the physical and…
To begin with, we identify the equations of elastostatics in a Riemannian manifold, which generalize those of classical elasticity in the three-dimensional Euclidean space. Our approach relies on the principle of least energy, which asserts…
This paper is devoted to the study of the one dimensional non homogeneous heat equation coupled to Dirichlet Boundary Conditions. We obtain the explicit expression of the solution of the linear equation by means of a direct integral in an…
This article deals with the efficient and accurate computation of the electrostatic forces between charged, spherical dielectric particles undergoing mutual polarisation. We use the spectral Galerkin boundary integral equation framework…
This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…
The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental…
This paper looks to apply the mathematical framework of the Theory of Functional Connections to the solution of boundary-value problems arising from hybrid systems. The Theory of Functional Connections is a technique to derive constrained…
Many boundary element integral equation kernels are based on the Green's functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell's equations.…
In this study, we consider the numerical solution of the Neumann initial boundary value problem for the wave equation in 2D domains. Employing the Laguerre transform with respect to the temporal variable, we effectively transform this…
In this article, the reproducing kernel Hilbert space [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast…
The purpose of this work is to show that there exists an additional invariance of the $\beta$-function equations of string theory on $d+1$-dimensional targets with $d$ toroidal isometries. It corresponds to a shift of the dilaton field and…