相关论文: A geometric formulation of the Shepard renormaliza…

In this article we consider resummed expressions for the heat-kernel's trace of a Laplace operator, the latter including a potential and imposing Dirichlet semitransparent boundary conditions on a surface of codimension one in flat space.…

In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology. The goal is the detection…

In this manuscript we present a detailed investigation of the form factors of boundary fields of the sinh-Gordon model with a particular type of Dirichlet boundary condition, corresponding to zero value of the sinh-Gordon field at the…

The computational cost of the boundary-condition-enforced immersed boundary method (IBM) increases in the order of $\mathcal{O}(N^2)$ as the number of Lagrangian points, $N$, increases. This is due to the time-consuming calculation of the…

A method is presented for the evaluation of integrals on tetrahedra where the integrand has an integrable singularity at one vertex. The approach uses a transformation to spherical polar coordinates which explicitly eliminates the…

The availability of a reliable bound on an integral involving the square of the modulus of a form factor on the unitarity cut allows one to constrain the form factor at points inside the analyticity domain and its shape parameters, and also…

A fundamental challenge in text-to-3D face generation is achieving high-quality geometry. The core difficulty lies in the arbitrary and intricate distribution of vertices in 3D space, making it challenging for existing models to establish…

A distributed optimal control problem with the constraint of a linear elliptic partial differential equation is considered. A necessary optimality condition for this problem forms a saddle point system, the efficient and accurate solution…

In this paper, we introduce a new method for applying the implicit function theorem to find nontrivial solutions to overdetermined problems with a fixed boundary (given) and a free boundary (to be determined). The novelty of this method…

Algorithms for initializing particle distribution in SPH simulations are important for improving simulation accuracy. However, no such algorithms exist for boundary integral SPH models, which can model complex geometries without requiring…

We provide a new algorithm for the treatment of the deconvolution problem on the sphere which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. We establish upper bounds for the…

Boundary value problems for integrable nonlinear evolution PDEs formulated on the finite interval can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this…

In this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local resolution analysis and show that the…

A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the…

This paper considers a fractional programming problem (P) which minimizes a ratio of quadratic functions subject to a two-sided quadratic constraint. As is well-known, the fractional objective function can be replaced by a parametric family…

It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the…

We consider the singular boundary-value problem \Delta u = f(u) in D; u|_dD= phi, where 1. D is a bounded C^2-domain of R^d, d >= 3 2. f: (0,1) -> (0,1) is a locally H\"older continuous function such that f(u) -> 1 as u -> 0 at the rate…

This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…

We give a fast, exact algorithm for solving Dirichlet problems with polynomial boundary functions on quadratic surfaces in R^n such as ellipsoids, elliptic cylinders, and paraboloids. To produce this algorithm, first we show that every…

We introduce the notion of radical parametrization of a surface, and we provide algorithms to compute such type of parametrizations for families of surfaces, like: Fermat surfaces, surfaces with a high multiplicity (at least the degree…