Retrieval of the piecewise-constant mass density in the Bergman wave equation

This investigation is concerned with the 2D acoustic scattering problem of a plane wave propagating in a non-lossy, isotropic, homogeneous fluid host and soliciting a linear, isotropic, macroscopically-homogeneous, generally-lossy, flat-plane layer in which the mass density and wavespeed are different from those of the host. The focus is on the inverse problem of the retrieval of the layer mass density. The data is the transmitted pressure field, obtained by simulation (resolution of the forward problem) in exact, explicit form via the domain integral form of the Bergman wave equation. This solution is exact and more explicit in terms of the mass-density contrast (between the host and layer) than the classical solution obtained by separation of variables. A perturbation technique enables the solution (in its form obtained by the domain integral method) to be cast as a series of powers of the mass density contrast, the first three terms of which are employed as the trial models in the treatment of the inverse problem. The aptitude of these models to retrieve the mass density contrast is demonstrated both theoretically and numerically.

PENENTUAN JENIS FUNGSI BASIS RADIAL DALAM DUAL RECIPROCITY BOUNDARY ELEMENT METHOD

Problems involving modified Helmholtz equation are considered in this paper. To solve the problem numerically, dual reciprocity boundary element method (DRBEM) is employed. Some stage have been passed, using reciprocal relation to approximate boundary integral and domain integral in modified Helmholtz equation . Until, linear equation system are obtained in matrix form. MATLAB is used to calculate the solutions of Solutions of are compared between the exact solution and the numerical solution of modified Helmholtz equation. The numerical results are based on the using of three types of radial basis function to approximate domain integral, such as polinomial, poliharmonik spline and linear types. The solutions show that the polinomial and poliharmonik spline types are more stable and approach to exact solution than linear types.

RINGS: Almost a ring, semiring, zero, integral domain

RING, commutative ring, almost a ring, semiring, zero ring, zero property, zero divisors, domain, integral domain, and their underlying definitions are presented in this white paper (knowledge base).