1,511 research outputs found
A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations
A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma
system is presented. The method uses a second or third order discontinuous
Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping
scheme. The method is benchmarked against an analytic solution of a dispersive
electron acoustic square pulse as well as the two-fluid electromagnetic shock
and existing numerical solutions to the GEM challenge magnetic reconnection
problem. The algorithm can be generalized to arbitrary geometries and three
dimensions. An approach to maintaining small gauge errors based on error
propagation is suggested.Comment: 40 pages, 18 figures
A space-time mixed Galerkin marching-on-in-time scheme for the time-domain combined field integral equation
The time domain combined field integral equation (TD-CFIE), which is constructed from a weighted sum of the time domain electric and magnetic field integral equations (TD-EFIE and TD-MFIE) for analyzing transient scattering from closed perfect electrically conducting bodies, is free from spurious resonances. The standard marching-on-in-time technique for discretizing the TD-CFIE uses Galerkin and collocation schemes in space and time, respectively. Unfortunately, the standard scheme is theoretically not well understood: stability and convergence have been proven for only one class of space-time Galerkin discretizations. Moreover, existing discretization schemes are nonconforming, i.e., the TD-MFIE contribution is tested with divergence conforming functions instead of curl conforming functions. We therefore introduce a novel space-time mixed Galerkin discretization for the TD-CFIE. A family of temporal basis and testing functions with arbitrary order is introduced. It is explained how the corresponding interactions can be computed efficiently by existing collocation-in-time codes. The spatial mixed discretization is made fully conforming and consistent by leveraging both Rao-Wilton-Glisson and Buffa-Christiansen basis functions and by applying the appropriate bi-orthogonalization procedures. The combination of both techniques is essential when high accuracy over a broad frequency band is required
Electro-rheological fluids under random influences: martingale and strong solutions
We study generalised Navier--Stokes equations governing the motion of an
electro-rheological fluid subject to stochastic perturbation. Stochastic
effects are implemented through (i) random initial data, (ii) a forcing term in
the momentum equation represented by a multiplicative white noise and (iii) a
random character of the variable exponent (as a result of a
random electric field). We show the existence of a weak martingale solution
provided the variable exponent satisfies ( in
two dimensions). Under additional assumptions we obtain also pathwise
solutions
On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces
In this paper the hp-version of the boundary element method is applied to the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. The underlying meshes are supposed to be quasi-uniform. We use \bH(\div)-conforming discretisations with quadrilateral elements of Raviart-Thomas type and establish quasi-optimal convergence of hp-approximations. Main ingredient of our analysis is a new \tilde\bH^{-1/2}(\div)-conforming p-interpolation operator that assumes only \bH^r\cap\tilde\bH^{-1/2}(\div)-regularity () and for which we show quasi-stability with respect to polynomial degrees
High-performance Parallel Solver for Integral Equations of Electromagnetics Based on Galerkin Method
A new parallel solver for the volumetric integral equations (IE) of
electrodynamics is presented. The solver is based on the Galerkin method which
ensures the convergent numerical solution. The main features include: (i) the
memory usage is 8 times lower, compared to analogous IE based algorithms,
without additional restriction on the background media; (ii) accurate and
stable method to compute matrix coefficients corresponding to the IE; (iii)
high degree of parallelism. The solver's computational efficiency is shown on a
problem of magnetotelluric sounding of the high conductivity contrast media. A
good agreement with the results obtained with the second order finite element
method is demonstrated. Due to effective approach to parallelization and
distributed data storage the program exhibits perfect scalability on different
hardware platforms.Comment: The main results of this paper were presented at IAMG 2015 conference
Frieberg, Germany. 28 pages, 11 figure
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