a finite volume solution to the geophysical electromagnetic forward problem using unstructured grids abstractthe application of unstructured grids can improve the solution of total field electromagnetic problems because these grids allow efficient local refinement of the mesh at the locations of high field gradients unstructured grids also provide the flexibility required for representing arbitrary topography and subsurface interfaces we investigated the generalization of the standard yee s staggered scheme to unstructured tetrahedral voronoi grids using a finite volume approach we discretized the helmholtz equation for the electric field in the frequency domain and solved the problem to find the projection of the total electric field along the edges of the tetrahedral elements to compute the electric and magnetic fields at the observation points an interpolation technique was employed which uses the edge vector interpolation functions of the tetrahedral elements to verify the presented scheme two examples were evaluated which revealed the computation of the total and secondary fields due to ele

locally conformal finite difference time domain techniques for particle in cell plasma simulation the dey mittra s dey r mitra a locally conformal finite difference time domain fdtd algorithm for modeling three dimensional perfectly conducting objects ieee microwave guided wave lett 7 273 1997 finite difference time domain partial cell method enables the modeling of irregularly shaped conducting surfaces while retaining second order accuracy we present an algorithm to extend this method to include charged particle emission and absorption in particle in cell codes several examples are presented that illustrate the possible improvements that can be realized using the new algorithm for problems relevant to plasma simulation

a method for incorporating gauss lasw into electromagnetic pic codes abstract an algorithm is presented which solves a modified set of maxwell s equations none of them elliptic in an electromagnetic pic type code the algorithm prevents large violations of gauss law by diffusing away numerical errors arising from the particle to grid apportionment method there are no restrictions on the manner in which charge and current densities are determined from the particle distribution in particular point particles and simple linear interpolation are used

on the extended error correcting capabilities of the quaternary preparata codes we prove extended error correcting capabilities of the quaternary preparata codes these are metrically reflected by a slight and simple modification of the lee distance on z sub 4 we change the weight of the element 2 to 4 3 and leave all remaining weights untouched

wavelet optimized finite difference mesh for mhd flow in a circular duct abstract there is a large class of important problems in scientific and engineering applications where the solution shows very little variation in the core region but very rapid changes close to the boundary of the domain of interest magnetohydrodynamic flow problems belong to this category treatment of such problems numerically therefore requires a non uniform mesh which is very fine near the boundary the determination of the size of the grid in different parts of the domain is therefore a challenging problem some recent studies suggest that wavelet methods can be effectively applied to create an optimized mesh the method has mostly been used for one dimensional problems the present paper investigates the problem for fully developed mhd duct flow problems which are basically two dimensional the boundary layer character is more pronounced in one direction as compared to the other the governing equations comprise a coupled system of two partial differential equations with dirichlet boundary conditions wavelet based adaptive mesh is first created and then the system is discretized over this mesh computations have been carried out at different precision levels for various hartmann numbers for a pipe of circular section contours are also drawn to depict the core and the boundary layer region

hybrid block amr in cartesian and curvilinear coordinates mhd applications abstract we present a novel hybrid block adaptive scheme for use in solving sets of near conservation laws in general orthogonal coordinate systems the adaptive mesh refinement amr scheme is block based i e individual grids have a pre fixed number of grid cells and is implemented for any dimensionality d its hybrid character relaxes the common approach where a block that needs refinement triggers 2 d subblocks when grids are refined by a factor of 2 this introduces incomplete families in the grid hierarchy but approaches the optimal fit to developing flow features inherent in the original patch based amr strategy our hybrid block amr approach is compared with a patch based amr one both exploiting openmp parallelism the implementation is able to handle general curvilinear coordinates for which restriction and prolongation formulae are presented along with boundary treatments at singular boundaries demonstrative examples cover hydro and magnetohydrodynamic mhd applications including tests on a 2d polar grid a 2 5d spherical and a 3d cylindrical configuration the applications cover classical up to relativistic mhd simulations of particular relevance for astrophysical magnetized jet and stellar wind studies

numerical solution to the time dependent maxwell equations in axisymmetric singular domains the singular complement method in this paper we present a method to solve numerically the axisymmetric time dependent maxwell equations in a singular domain in math methods appl sci 25 2002 49 math methods appl sci 26 2003 861 the mathematical tools and an in depth study of the problems posed in the meridian half plane were exposed the numerical method and experiments based on this theory are now described here it is also the generalization to axisymmetric problems of the singular complement method that we developed to solve maxwell equations in 2d singular domains see c r acad sci paris t 330 2000 391 it is based on a splitting of the space of solutions in a regular subspace and a singular one derived from the singular solutions of the laplace problem numerical examples are finally given to illustrate our purpose in particular they show how the singular complement method captures the singular part of the solution

using rationalized haar wavelet for solving linear integral equations the main purpose of this paper is to demonstrate that using rationalized haar wavelet for solving linear fredholm integral equation of the second kind we convert the integral equation to a system of linear equations and by using numerical examples we show our estimation have a good degree of accuracy

an unsplit cell centered godunov method for ideal mhd we present a second order godunov algorithm for multidimensional ideal mhd our algorithm is based on the unsplit formulation of colella j comput phys 87 1990 with all of the primary dependent variables centered at the same location to properly represent the divergence free condition of the magnetic fields we apply a discrete projection to the intermediate values of the field at cell faces and apply a filter to the primary dependent variables at the end of each time step we test the method against a suite of linear and nonlinear tests to ascertain accuracy and stability of the scheme under a variety of conditions the test suite includes rotated planar linear waves mhd shock tube problems low beta flux tubes and a magnetized rotor problem for all of these cases we observe that the algorithm is second order accurate for smooth solutions converges to the correct weak solution for problems involving shocks and exhibits no evidence of instability or loss of accuracy due to the possible presence of non solenoidal fields

a fourth order accurate method for the incompressible navier stokes equations on overlapping grids a method is described to solve the time dependent incompressible navier stokes equations with finite differences on curvilinear overlapping grids in two or three space dimensions the scheme is fourth order accurate in space and uses the momentum equations for the velocity coupled to a poisson equation for the pressure the boundary condition for the pressure is taken as u 0 extra numerical boundary conditions are chosen to make the scheme accurate and stable the velocity is advanced explicitly in time any standard time stepping scheme such as runge kutta can be used the poisson equation is solved using direct or iterative sparse matrix solvers or by the multigrid algorithm computational results in two and three space dimensions are given

solving second kind integral equations by galerkin methods with continuous orthogonal wavelets abstract in this paper we use the continuous wavelets on the interval constructed by cohen et al appl comput harm anal 1 1993 54 81 to solve the second kind integral equations to this end we give the decomposition and reconstruction algorithm for these wavelets and construct the quadrature formulae for the calculation of inner products of any functions and the scaling functions which are required in the wavelet galerkin methods for integral equations in this method the integral kernels are represented in these wavelet bases as sparse matrices to high precision thus we present an efficient algorithm for numerical solution of second kind integral equations

the z sub 4 linearity of kerdock preparata goethals and related codes certain notorious nonlinear binary codes contain more codewords than any known linear code these include the codes constructed by nordstrom robinson 1967 kerdock 1972 preparata 1968 goethals 1974 and delsarte goethals 1975 it is shown here that all these codes can be very simply constructed as binary images under the gray map of linear codes over z sub 4 the integers mod 4 although this requires a slight modification of the preparata and goethals codes the construction implies that all these binary codes are distance invariant duality in the z sub 4 domain implies that the binary images have dual weight distributions the kerdock and preparata codes are duals over z sub 4 and the nordstrom robinson code is self dual which explains why their weight distributions are dual to each other the kerdock and preparata codes are z sub 4 analogues of first order reed muller and extended hamming codes respectively all these codes are extended cyclic codes over z sub 4 which greatly simplifies encoding and decoding an algebraic hard decision decoding algorithm is given for the preparata code and a hadamard transform soft decision decoding algorithm for the i kerdock code binary first and second order reed muller codes are also linear over z sub 4 but extended hamming codes of length n spl ges 32 and the golay code are not using z sub 4 linearity a new family of distance regular graphs are constructed on the cosets of the preparata code

a finite volume method for the approximation of maxwell s equations in two space dimensions on arbitrary meshes a new finite volume method is presented for discretizing the two dimensional maxwell equations this method may be seen as an extension of the covolume type methods to arbitrary possibly non conforming or even non convex n sided polygonal meshes thanks to an appropriate choice of degrees of freedom an equivalent formulation of the scheme is given in terms of discrete differential operators obeying discrete duality principles the main properties of the scheme are its energy conservation its stability under a cfl like condition and the fact that it preserves gauss law and divergence free magnetic fields second order convergence is demonstrated numerically on non conforming and distorted meshes

translates of linear codes over z sub 4 we give a method to compute the complete weight distribution of translates of linear codes over z sub 4 the method follows known ideas that have already been used successfully by others for hamming weight distributions for the particular case of quaternary preparata codes we obtain that the number of distinct complete weights for the dual preparata codes and the number of distinct complete coset weight enumerators for the preparata codes are both equal to ten independent of the code length

phase accuracy comparisons and improved far field estimates for 3 d edge elements on tetrahedral meshes abstract edge element methods have proved very effective for 3 d electromagnetic computations and are widely used on unstructured meshes however the accuracy of standard edge elements can be criticised because of their low order this paper analyses discrete dispersion relations together with numerical propagation accuracy to determine the effect of tetrahedral shape on the phase accuracy of standard 3 d edge element approximations in comparison to other methods scattering computations for the sphere obtained with edge elements are compared with results obtained with vertex elements and a new formulation of the far field integral approximations for use with edge elements is shown to give improved cross sections over conventional formulations

electromagnetics via the taylor galerkin finite element method on unstructured grids traditional techniques for computing electromagnetic solutions in the time domain rely on finite differences these so called fdtd finite difference time domain methods are usually defined only on regular lattices of points and can be too restrictive for geometrically demanding problems great geometric flexibility can be achieved by abandoning the regular latticework of sample points and adopting an unstructured grid an unstructured grid allows one to place the grid points anywhere one chooses so that curved boundaries can be fit with ease and local regions in which the field gradients are steep can be selectively resolved with a fine mesh in this paper we present a technique for solving maxwell s equations on an unstructured grid based on the taylor galerkin finite element method we present several numerical examples which reveal the fundamental accuracy and adaptability of the method although our examples are in two dimensions the techniques and results generalize readily to 3d

a positive muscl hancock scheme for ideal magnetohydrodynamics we present a highly robust second order accurate scheme for the euler equations and the ideal mhd equations the scheme is of predictor corrector type with a muscl scheme following as a special case the crucial ingredients are an entropy stable approximate riemann solver and a new spatial reconstruction that ensures positivity of mass density and pressure for multidimensional mhd a new discrete form of the powell source terms is vital to ensure the stability properties the numerical examples show that the scheme has superior stability compared to standard schemes while maintaining accuracy in particular the method can handle very low values of pressure i e low plasma b or high mach numbers and low mass densities

on z sub 4 and z sub 9 linear lifts of the golay codes in this paper we investigate z sub 4 linear and z sub 9 linear lifts of the extended binary and ternary golay codes we introduce weight functions on z sub 4 and z sub 9 which reflect previously unknown error correcting and packing capabilities of these codes we compare their properties with those of the hamming lee and homogeneous weights and give algebraic decoding schemes using a general decoder

ideal glm mhd about the entropy consistent nine wave magnetic field divergence diminishing ideal magnetohydrodynamics equations abstract the paper presents two contributions in the context of the numerical simulation of magnetized fluid dynamics first we show how to extend the ideal magnetohydrodynamics mhd equations with an inbuilt magnetic field divergence cleaning mechanism in such a way that the resulting model is consistent with the second law of thermodynamics as a byproduct of these derivations we show that not all of the commonly used divergence cleaning extensions of the ideal mhd equations are thermodynamically consistent secondly we present a numerical scheme obtained by constructing a specific finite volume discretization that is consistent with the discrete thermodynamic entropy it includes a mechanism to control the discrete divergence error of the magnetic field by construction and is galilean invariant we implement the new high order mhd solver in the adaptive mesh refinement code flash where we compare the divergence cleaning efficiency to the constrained transport solver available in flash unsplit staggered mesh scheme

a block preconditioner for an exact penalty formulation for stationary mhd the magnetohydrodynamics mhd equations are used to model the flow of electrically conducting fluids in such applications as liquid metals and plasmas this system of non self adjoint nonlinear pdes couples the navier stokes equations for fluids and maxwell s equations for electromagnetics there has been recent interest in fully coupled solvers for the mhd system because they allow for fast steady state solutions that do not require pseudo time stepping when the fully coupled system is discretized the strong coupling can make the resulting algebraic systems difficult to solve requiring effective preconditioning of iterative methods for efficiency in this work we consider a finite element discretization of an exact penalty formulation for the stationary mhd equations posed in two dimensional domains this formulation has the benefit of implicitly enforcing the divergence free condition on the magnetic field without requiring a lagrange multiplier we consider extending block preconditioning techni

high order well balanced finite volume schemes for simulating wave propagation in stratified magnetic atmospheres wave propagation in idealized stellar atmospheres is modeled by the equations of ideal mhd together with the gravity source term the waves are modeled as small perturbations of isothermal steady states of the system we consider a formulation of ideal mhd based on the godunov powell form with an embedded potential magnetic field appearing as a parameter the equations are discretized by finite volume schemes based on approximate riemann solvers of the hll type and upwind discretizations of the godunov powell source terms local hydrostatic reconstructions and suitable discretization of the gravity source term lead to a well balanced scheme i e a scheme which exactly preserves a discrete version of the relevant steady states higher order of accuracy is obtained by employing suitable minmod eno and weno reconstructions based on the equilibrium variables to construct a well balanced scheme the resulting high order well balanced schemes are validated on a suite of numerical experiments involving complex magnetic fields the schemes are observed to be robust and resolve the complex physics well

two coupled particle finite volume methods using delaunay voronoi meshes for the approximation of vlasov poisson and vlasov maxwell equations this paper deals with the approximation of vlasov poisson and vlasov maxwell equations we present two coupled particle finite volume methods which use the properties of delaunay voronoi meshes these methods are applied to benchmark calculations and engineering problems such as simulation of electron injector devices

gauss s law satisfying energy conserving semi implicit particle in cell method abstract the energy conserving semi implicit method ecsim introduced by lapenta 2017 has many advantageous properties compared to the classical semi implicit and explicit pic methods most importantly energy conservation eliminates the growth of the finite grid instability we have implemented ecsim in a different and more efficient manner than the original approach more importantly we have addressed two major shortcomings of the original ecsim algorithm there is no mechanism to enforce gauss s law and there is no mechanism to reduce the numerical oscillations of the electric field a classical approach to satisfy gauss s law is to modify the electric field and its divergence using either an elliptic or a parabolic hyperbolic correction based on the generalized lagrange multiplier method this correction however violates the energy conservation property and the oscillations related to the finite grid instability reappear in the modified ecsim scheme we invented a new alternative approach the particle positions are modified instead of the electric field in the correction step displacing the particles slightly does not change the energy conservation property while it can satisfy gauss s law by changing the charge density we found that the new gauss s law satisfying energy conserving semi implicit method gl ecsim produces superior results compared to the original ecsim algorithm in some simulations however there are still some numerical oscillations present in the electric field we attribute this to the simple finite difference discretization of the energy conserving implicit electric field solver we modified the spatial discretization of the field solver to reduce these oscillations while only slightly violating the energy conservation properties we demonstrate the improved quality of the gl ecsim method with several tests

a wavelet method for solving singular integral equation of mhd this paper presents haar wavelet approximation to solve a singular integral equation which has singularities on a diagonal of the domain r 1 1 x 1 1 the singularities arise basically due to modified bessel function k 0 which appears as a part of the kernel thus the integral equation is weakly logarithmically singular only the problem is solved considering all the singularities of the kernel and results are examined for approximations of different orders our interest to solve the problem using haar wavelet basis is due to its simplicity and efficiency in numerical approximation the results show convergence trend as mesh is refined comparison is made with some available results obtained earlier by partial consideration of the singularities

a finite volume particle in cell method for the numerical treatment of maxwell lorentz equations on boundary fitted meshes a new conceptual framework solving numerically the time dependent maxwell lorentz equations on a non rectangular quadrilateral mesh in two space dimensions is presented beyond a short review of the applied particle treatment based on the particle in cell method a finite volume scheme for the numerical approximation of the maxwell equations is introduced using non rectangular quadrilateral grid arrangements the coupling of a high resolution fv maxwell solver with the pic method is a new approach in the context of self consistent charged particle simulation in electromagnetic fields furthermore first simulation results of the time dependent behaviour of an externally applied b ion diode developed at the forschungszentrum in karlsruhe are presented copyright 1999 john wiley sons ltd

a stable projection method for the incompressible navier stokes equations on arbitrary geometries and adaptive quad octrees we present a numerical method for solving the incompressible navier stokes equations on non graded quadtree and octree meshes and arbitrary geometries the viscosity is treated implicitly through a finite volume approach based on voronoi partitions while the convective term is discretized with a semi lagrangian scheme thus relaxing the restrictions on the time step a novel stable implementation of the projection step is introduced making use of the marker and cell layout for the data the solver is validated numerically in two and three spatial dimensions

edge element methods for maxwell s equations with strong convergence for gauss laws in this paper we propose and investigate some edge element approximations for three maxwell systems in three dimensions the stationary maxwell equations the time harmonic maxwell equations and the time dependent maxwell equations these approximations have three novel features first the resulting discrete edge element systems can be solved by some existing preconditioned solvers with optimal convergence rate independent of nite element meshes including the stationary maxwell equations second they ensure the optimal strong convergence of the gauss laws in some appropriate norm in addition to the standard optimal convergence in energy norm under the general weak regularity assumptions that hold for both convex and non convex polyhedral domains and for the discontinuous coecients that may have large jumps across the interfaces between dierent media finally no saddle point discrete systems are needed to solve for the stationary maxwell equations unlike most existing edge element schemes

nonlinear magnetohydrodynamics simulation using high order finite elements a conforming representation composed of 2d finite elements and finite fourier series is applied to 3d nonlinear non ideal magnetohydrodynamics using a semi implicit time advance the self adjoint semi implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments growth rates for resistive tearing modes with experimentally relevant lundquist number are computed accurately with time steps that are large with respect to the global alfven time and moderate spatial resolution when the finite elements have basis functions of polynomial degree p two or larger an error diffusion method controls the generation of magnetic divergence error convergence studies show that this approach is effective for continuous basis functions with p 2 where the number of test functions for the divergence control terms is less than the number of degrees of freedom in the expansion for vector fields anisotropic thermal conduction at realistic ratios of parallel to perpendicular conductivity is computed accurately with p 3 without mesh alignment a simulation of tearingmode evolution for a shaped toroidal tokamak equilibrium demonstrates the effectiveness of the algorithm in nonlinear conditions and its results are used to verify the accuracy of the numerical anisotropic thermal conduction in 3d magnetic topologies

numerical solution to the time dependent maxwell equations in two dimensional singular domains in this paper we present a method to solve numerically the time dependent maxwell equations in nonsmooth and nonconvex domains indeed the solution is not of regularity h1 in space in general moreover the space of h1 regular fields is not dense in the space of solutions thus an h1 conforming finite element method can fail even with mesh refinement the situation is different than in the case of the laplace problem or of the lame system for which mesh refinement or the addition of conforming singular functions work to cope with this difficulty the singular complement method is introduced this method consists of adding some well chosen test functions these functions are derived from the singular solutions of the laplace problem also the scm preserves the interesting features of the original method easiness of implementation low memory requirements small cost in terms of the cpu time to ascertain its validity some concrete problems are solved numerically