A fast multipole boundary element method (BEM) for solving large-scale thin plate bending problems is presented in this paper. The method is based on the Kirchhoff thin plate bending theory and the biharmonic equation governing the deflection of the plate. First, the direct boundary integral equations and the conventional BEM for thin plate bending problems are reviewed. Second, the complex not...

The lowest-order nonlocal small slope approximation (NLSSA) reflection coefficient is derived, and numerical results are presented for one-dimensional (1-D) surfaces, satisfying the Dirichlet boundary condition. Reduction to the perturbation expression occurs in the small height limit, and the first term of the reflection coefficient gives the Kirchhoff approximation (KA) result. Numerical resu...

Wave field synthesis (WFS) is a technique aiming at the reproduction of a desired sound field. It is based on the Kirchhoff-Helmholtz integral formulated for interior problems [1]. This implies that WFS is per se only capable of recreating the wave field generated by events outside the listening area. In particular, the traditional WFS literature (e.g. [2]) focuses on the reproduction of the so...

First, we show the equivalence of two definitions left Riemann–Liouville fractional integral on time scales. Then, establish and characterize Sobolev space with help notion derivative At same time, define weak derivatives demonstrate that they coincide ones Next, prove kinds norms in introduced derive its completeness, reflexivity, separability, some embedding. Finally, as an application, by co...

The capacitance of the circular parallel plate capacitor is calculated by expanding the solution to the Love integral equation into a Fourier cosine series. Previously, this kind of expansion has been carried out numerically, resulting in accuracy problems at small plate separations. We show that this bottleneck can be alleviated, by calculating all expansion integrals analytically in terms of ...

A typical imaging condition for seismic reflection data involves source and receiver wavefield matching, e.g. by cross-correlation, at every image location. This statement is true no matter how the two wavefields are reconstructed, for example by one-way wavefield extrapolation, or two-way reverse-time extrapolation, or Kirchhoff integral methods. This statement is also true when the source and...

Accurate rendering of spatial audio over headphones requires the use of personalized head related transfer functions (HRTFs). These HRTFs are difficult to obtain due to the tedious and expensive measurement process requiring an anechoic chamber. An alternate approach uses accurate 3D meshes of human head and torso and numerical simulation techniques to compute personalized HRTFs. While these si...

Comparisons are made between calculated and measured angle-resolved light-scattering distributions from clear dielectric isotropic epoxy coatings over a range of rms roughness conditions, resulting in strongly specular scattering to diffuse scattering characteristics. Calculated distributions are derived from topography measurements performed with interferometric microscopes. Two methods of cal...

AbsfrucfA novel algorithm designed to compute efficiently and accurately the high-frequency electromagnetic scattering from open-ended waveguide cavities is presented. The cavity is converted into a stepped-waveguide model so that the field spectra are propagated, forward and backward, along each waveguide section. As boundary conditions for perfect electric conductors are applied via image the...