We use the method of layer potentials to study interior and exterior Dirichlet and Neumann problems for the Helmholtz equation ( +k)u = 0 on a Lipschitz domain for all wave number k 2C with Imk 0. Following the approach for the case of smooth boundary [3], we pursue as solution a single layer potential for Neumann problem or a double layer potential for Dirichlet problem. The lack of smoothness...

The elasticity mixed boundary values problems dealing with half-space contact are generally well resolved. A large number of these solutions are obtained by using the integral transformation method and methods based the integral equations. However, the problems of finite layer thicknesses are less investigated, despite their practical interests. This study resolves a quasi-stationary problem of...

The total dissipation rate for magnetohydrodynamic (MHD) flows in plane geometry with both velocity and magnetic shear is studied. For some boundary conditions it is shown that the lower bound on the dissipation rate is achieved by the equivalent of Stokes flow for MHD. Using the ‘background method’ (Doering & Constantin, Phys. Rev. Lett. 69, 1648–1651 (1992)) upper bounds for the dissipation r...

The total dissipation rate for magnetohydrodynamic ~MHD! flows in plane geometry with both velocity and magnetic shear is studied. For some boundary conditions it is shown that the lower bound on the dissipation rate is achieved by the equivalent of Stokes flow for MHD. Using the background method @Doering and Constantin, Phys. Rev. Lett. 69, 1648 ~1992!# upper bounds for the dissipation rate a...

mhd boundary layer flow of two phase model nanofluid over a vertical plate is investigated both analytically and numerically. a system of governing nonlinear partial differential equations is converted into a set of nonlinear ordinary differential equations by suitable similarity transformations and then solved analytically using homotopy analysis method and numerically by the fourth order rung...

It is well-known that magnetic fields dominate the dynamics in solar corona, and new generation of numerical modeling evolution coronal fields, as featured with boundary conditions driven directly by observation data, are being developed. This paper describes a approach data-driven magnetohydrodynamic (MHD) simulation active region (AR) field evolution, which for first time full-MHD model utili...

finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. however, the coupling of these two methods happens to be more efficient as it combinestheir merits. in this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the helmholtz equation is presented.

Explicit expressions have been derived for momentum and thermal boundary-layer thickness of the laminar, uniform stagnation flows characteristic of highly convective chemical vapor deposition pedestal reactors. Expressions for the velocity and temperature profiles within the boundary layers have also been obtained. The results indicate that, to leading order, the momentum boundary-layer thickne...

A hierarchical multilevel preconditioner is constructed for an efficient solution of a first kind boundary integral equation with the single layer potential operator discretized by a boundary element method. This technique is based on a hierarchical clustering of all boundary elements as used in fast boundary element methods. This hierarchy is applied to define a sequence of nested boundary ele...

Our understanding of the dynamical processes which control the structure and evolution of the interaction region between an accretion disk and the central star is reviewed. If the central star is unmagnetized, this interaction is in the form of a classical boundary layer. However, if the central star is strongly magnetized, it is expected that the inner disk is truncated by the stellar field, a...