相关论文: A New Model for Solving Narrow Escape Problem in D…

Reduction of computational cost of solutions is a key issue to crack identification or crack propagation problems. One of the solution is to avoid re-meshing the domain when the crack position changes or when the crack extends. To avoid…

We present a waveform relaxation version of the Dirichlet-Neumann method for parabolic problem. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-overlapping spatial domain decomposition, and the iteration…

In this paper, we present numerical methods to implement the probabilistic representation of third kind (Robin) boundary problem for the Laplace equations. The solution is based on a Feynman-Kac formula for the Robin problem which employs…

A new numerical method is developed to approximate the solution of Laplace's equation in the exterior of the sphere with a strongly nonlinear boundary value of oblique type. A functional analysis attempt to solve this type of boundary…

We construct a multiply connected domain in $\mathbb{R}^2$ for which the second eigenfunction of the Laplacian with Robin boundary conditions has an interior nodal line. In the process, we adapt a bound of Donnelly-Fefferman type to obtain…

We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum of the solution is greater than 0, and some other families of domains were it is…

Motivated by the paraxial narrow-angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schr\"odinger-type equation posed on…

We revisit the problem of identifying an unknown portion of a boundary subject to a Robin condition based on a pair of Cauchy data on the accessible part of the boundary. It is known that a single measurement may correspond to infinitely…

A nonuniform Neumann boundary-value problem is considered for the Poisson equation in a thin domain $\Omega_\varepsilon$ coinciding with two thin rectangles connected through a joint of diameter ${\cal O}(\varepsilon)$. A rigorous procedure…

We deal with the existence of weak solutions for a mixed Neumann-Robin-Cauchy problem. The existence results are based on global-in-time estimates of approximating solutions, and the passage to the limit exploits compactness techniques. We…

The first part of the course is devoted to the study of solutions to the Laplace equation in $\Omega\setminus K$, where $\Omega$ is a two-dimensional smooth domain and $K$ is a compact one-dimensional subset of $\Omega$. The solutions are…

Systems with non-Hermitian skin effects are very sensitive to the imposed boundary conditions and lattice size, and thus an important question is whether non-Hermitian skin effects can survive when deviating from the open boundary…

This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…

A general topic of current interest is the analysis of diffusion problems in singularly perturbed domains with small interior targets or traps (the narrow capture problem). One major application is to intracellular diffusion, where the…

We generalize the technique of [Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains, SIAM J. Sci. Comput. 34, pp. A497--A519 (2012)] to elliptic problems with mixed boundary conditions and elliptic…

This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order…

The long-time asymptotic behavior of solutions to the focusing nonlinear Schr\"odinger (NLS) equation on the line with symmetric, nonzero boundary conditions at infinity is studied in the case of initial conditions that allow for the…

We consider steady-state diffusion in a three-dimensional bounded domain with a smooth reflecting boundary that is partially covered by small partially reactive patches. By using the method of matched asymptotic expansions, we investigate…

We prove several results for the Dirichlet, Neumann and Regularity problems for the Laplace equation in graph Lipschitz domains in the plane, considering $A_{\infty}$-measures on the boundary. More specifically, we study the…

In this paper, we study the computational question of whether the Steklov spectrum of smooth simply connected planar domains can be approximated accurately by a boundary-only formulation based on harmonic conjugation. For the unit disk, the…