On electron kinetic scales, ions and electrons decouple, velocity shear on inertial length ∼de can trigger electromagnetic (EM) Kelvin–Helmholtz instability (EKHI). In this paper, we present an analytic study of EM EKHI in inviscid collisionless plasma with a step-function flow. We show that incompressible plasma, the ideal frozen-in condition E+ve×B/c=0 must be broken for to occur. flow, is re...

The numerical solution of Helmholtz’ equation at large wavenumber is very expensive if attempted by ”traditional” discretisation methods (FDM, standard Galerkin FEM). For reliable results, the mesh has to be very fine. The bad performance of the traditional FEM for Helmholtz problems can be related to the deterioration of stability of the Helmholtz differential operator at high wavenumber. As a...

Operator symbols play a pivotal role in both the exact, well-posed, one-way reformulation of solving the (elliptic) Helmholtz equation and the construction of the generalized Bremmer coupling series. The inverse square-root and square-root Helmholtz operator symbols are the initial quantities of interest in both formulations, in addition to providing the theoretical framework for the developmen...

The Cauchy problem for Helmholtz equation arises from inverse scattering problems. Specific backgrounds can be seen in the existing literature; we can refer to 1–6 and so forth. A number of numerical methods for stabilizing this problem are developed. Several boundary element methods combined with iterative, conjugate gradient, Tikhonov regularization, and singular value decomposition methods a...