Estimation of sediment thickness by solving Poisson's equation with bedrock outcrops as boundary conditions

Solving wave equation with spectral methods and nonreflecting boundary conditions

A multidomain spectral method for solving wave equations is presented. This method relies on the expansion of functions on basis of spherical harmonics (Y m l (θ, φ)) for the angular dependence and of Chebyshev polynomials Tn(x) for the radial part. The spherical domains consist of shells surrounding a nucleus and cover the space up to a finite radius R at which boundary conditions are imposed....

Integral Equation Methods for Solving Laplace's Equation with Nonlinear Boundary Conditions: the Smooth Boundary Case

A nonlinear boundary value problem for Laplace's equation is solved numerically by using a reformulation as a nonlinear boundary integral equation. Two numerical methods are proposed and analyzed for discretizing the integral equation, both using product integration to approximate the singular integrals in the equation. The first method uses the product Simpson's rule, and the second is based o...

Analysis of Free Vibration of Triangular Plates with Non-Uniform Linear Thickness and Arbitrary Boundary Conditions

Analysis of Free Vibration of Triangular Plates with Non-Uniform Linear Thickness and Arbitrary Boundary Conditions

Solving Poisson's Equation with Interior Conditions

We consider the problem of extending the solution of a particular two-dimensional Poisson equation to a larger domain. This problem is related to the problem of putting a non-neutral plasma into equilibrium by applying a suitable wall potential, and to similar problems in two-dimensional °uid dynamics. While one cannot always ̄nd an exact solution, one can always ̄nd an approximate solution if th...