Abstract The development of a fast multipole method accelerated iterative solution of the boundary element equations for large problems involving hundreds of thousands elements for the Helmholtz equations in 3D is described. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements) and the convergence criterion for iterative c...

In this paper, we prove the existence and stability of subsonic flows for steady full Euler-Poisson system in a two dimensional nozzle of finite length when imposing the electric potential difference on non-insulated boundary from a fixed point at the entrance, and prescribing the pressure at the exit of the nozzle. The Euler-Poisson system for subsonic flow is a hyperbolic-elliptic coupled non...

Elastic wave propagation in anisotropic media is well represented by elastic wave equations. Modeling based on elastic wave equations characterizes both kinematics and dynamics correctly. However, because P and S modes are both propagated using elastic wave equations, there is a need to separate P and S modes to obtain clean elastic images. The separation of wave modes to P and S from isotropic...

We present a joint acoustic/seismic inverse scattering and finite-frequency (reflection) tomography program, formulated as a coupled set of optimization problems, in terms of inhomogeneous Helmholtz equations. We use a higher order finite difference scheme for these Helmholtz equations to guarantee sufficient accuracy. We adapt a structured approximate direct solver for the relevant systems of ...

Thermodynamic and dynamic analyses of a variable speed reciprocating compressor have been conducted to investigate performance changes and some data related to the reliability problems such as valve velocity, PV value, bearing loci, Sommerfeld number, minimum film thickness etc. The first law of thermodynamics, continuity equations, valve dynamic equations and Helmholtz resonator method were us...

The essence of the boundary-field equation method is the reduction of the boundary value problem under consideration to an equivalent nonlocal boundary value problem in a bounded domain by using boundary integral equations. The latter can then be treated by the standard variational method including its numerical approximations. In this paper, various formulations of the nonlocal boundary value ...

Abstract. We consider the discretization and approximate solution of inhomogeneous anisotropic ‘Helmholtz’ equations in 3D. The anisotropy comprises general (tilted) TI symmetries. In particular, we are concerned with solving these equations on a large domain, for a large number of different sources. We make use of a nested dissection based domain decomposition in a massively parallel multifron...

We consider the Helmholtz transmission problem with piecewise-constant material coefficients, and standard associated direct boundary integral equations. For certain coefficients geometries, norms of inverses operators grow rapidly through an increasing sequence frequencies, even though this is not case for solution operator problem; we call phenomenon that spurious quasi-resonances. give a rig...

The transfer of heat due to the emission of electromagnetic waves is called thermal radiations. In local fractional calculus, there are numerous contributions of scientists, like Mandelbrot, who described fractal geometry and its wide range of applications in many scientific fields. Christianto and Rahul gave the derivation of Proca equations on Cantor sets. Hao et al. investigated the Helmholt...

We describe a multiresolution solver for the all-electron local density approximation Kohn-Sham equations for general polyatomic molecules. The resulting solutions are obtained to a user-specified precision and the computational cost of applying all operators scales linearly with the number of parameters. The construction and use of separated forms for operators (here, the Green's functions for...