a time domain unstructured grid approach to the simulation of electromagnetic scattering in piecewise homogeneous media abstract the simulation of the scattering of plane electromagnetic waves by obstacles constructed from piecewise homogeneous material media is considered the governing equations are maxwell s equations which are expressed in a conservation form the solution is obtained on a grid consisting of an unstructured assembly of linear triangular elements in 2d by modifying a technique developed originally for the solution of the compressible euler equations the computed solution is used to determine the radar scattering width of the obstacle

an ergodic theorem for semigroups of nonexpansive mappings in a hilbert space abstract j b baillon c r acad sci paris ser a 280 1975 1511 1514 proved an ergodic theorem for a single nonexpansive mapping in a hilbert space which is a nonlinear version of von neumann s mean ergodic theorem in this paper we study the ergodic behavior of a semigroup of nonexpansive mappings we try to find a sequence of means on the semigroup generalizing the cesaro means on n such that the corresponding sequence of nonexpansive mappings converges to a projection onto the set of common fixed points our method of proof is an appropriate modification of a pazy s proof israel j math 26 1977 197 204 of baillon s theorem

efficient three dimensional delaunay triangulation with automatic point creation and imposed boundary constraints a method is described which constructs three dimensional unstructured tetrahedral meshes using the delaunay triangulation criterion several automatic point creation techniques will be highlighted and an algorithm will be presented which can ensure that given an initial surface triangulation which bounds a domain a valid boundary conforming assembly of tetrahedra will be produced statistics of measures of grid quality are presented for several grids the efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities

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

a stitching method for the generation of unstructured meshes for use with co volume solution techniques abstract the successful implementation of co volume time domain solution techniques requires the use of high quality smooth dual meshes the generation of delaunay voronoi diagrams with these properties for two dimensional domains of complicated geometrical shape is considered in the adopted approach near boundary regions are discretised according to prescribed criteria and the remainder of the computational domain is discretised using an ideal mesh the two meshes are stitched together to provide a consistent mesh for the complete domain after smoothing the resulting mesh is found to be of a quality which exceeds that of meshes produced by standard automatic unstructured mesh generation methods examples involving electromagnetic wave scattering are included to demonstrate the computational performance that can be achieved with a co volume time domain solution algorithm on these meshes

nonexpansive retractions and nonlinear ergodic theorems in banach spaces on donne des theoremes ergodiques non lineaires pour des semigroupes commutatifs d applications non dilatation sans utiliser le concept de moyenne compacte

parallel processing for the simulation of problems involving scattering of electromagnetic waves abstract the three dimensional simulation of the scattering of electromagnetic waves by obstacles of arbitrary geometrical shape is considered maxwell s curl equations are solved in the time domain on an unstructured mesh of linear tetrahedral elements the discrete equations are formed by a galerkin procedure with a lax wendroff consistent numerical flux function and explicit time stepping parallelisation of the procedure is achieved by mesh decomposition and the use of a single program multiple data model the approach is first validated and is then applied to problems involving the scattering of plane electromagnetic waves by a complete aircraft

arbitrary order edge elements for electromagnetic scattering simulations using hybrid meshes and a pml the use of arbitrary order edge elements for the simulation of two dimensional electromagnetic scattering problems on hybrid meshes of triangles and quadrilaterals is described single frequency incident waves generated by a source in the far field are considered and the solution is determined in the frequency domain for numerical simulation the solution domain is truncated at a finite distance from the perfectly conducting scatterer and the non reflecting boundary condition at the truncated boundary is imposed by the use of a perfectly matched layer pml several examples are included to demonstrate the performance of the proposed procedure copyright 2002 john wiley sons ltd

delaunay triangulation in computational fluid dynamics abstract a method which utilises the delaunay criterion is described by which computational grids consisting of assemblies of triangles or tetrahedra can be constructed an algorithm is briefly outlined to construct the triangulation and its dual the voronoi diagram issues related to how to construct boundary conforming grids from such a triangulation are addressed and details are presented of how grid points within the domain can be generated automatically the point generation algorithm utilises either the given boundary point distribution or for grid adaption a background mesh computational aspects of constructing the triangulation in both 2 and 3 dimensions are covered examples of meshes and flow computations for a range of aerospace geometries are presented

a mean ergodic theorem for nonlinear semigroups which are asymptotically nonexpansive in the intermediate sense abstract let x be a uniformly convex banach space such that its dual x has the kadec klee property c a bounded closed convex subset of x and t t t t 0 a one parameter nonlinear semigroup which is asymptotically nonexpansive in the intermediate sense we show that every continuous almost orbit of t is weakly almost convergent to a common fixed point of t a discrete version of our main result is also included

asymptotic behavior of commutative semigroups of nonexpansive mappings in banachspaces on etablit des theoremes de convergence pour des semigroupes generaux d applications non dilatation dans le cadre des espaces de banach on demontre un theoreme ergodique non lineaire de type rode pour des semigroupes commutatifs

kloosterman sums for chevalley groups a generalization of kloosterman sums to a simply connected chevalley group g is discussed these sums are parameterized by pairs w t where w is an element of the weyl group of g and t is an element of a q split torus in g the sl 2 q kloosterman sums coincide with the classical kloosterman sums and sl r q kloosterman sums r 3 coincide with the sums introduced in b f g f s algebraic properties of the sums are proved by root system methods in particular an explicit decomposition of a general kloosterman sum over q into the product of local p adic factors is obtained using this factorization one can show that the kloosterman sums corresponding to a toral element which acts trivially on the highest weight space of a fundamental irreducible representation splits into a product of kloosterman sums for chevalley groups of lower rank

the retractions onto the common fixed points of some families and semigroups of mappings abstract assume that c is a closed convex subset of a reflexive banach space e and t i i i is a family of self mappings on c of type such that f the common fixed point set of is nonempty from our results in this paper it can be derived that a if i i f t i is contained in a 3 dimensional subspace of e then f is a nonexpansive retract of c b if is commutative there exists a retraction r of type from c onto f such that r t i t i r r i and every closed convex invariant subset of c is r invariant the same result holds for a non commutative right amenable semigroup under some additional assumptions moreover the existence of a t i ergodic retraction r of type from c x i l e x i c i i onto f in l e for the family is discussed we also apply some of our results to find ergodic retractions for nonexpansive affine mappings

a parallel implicit explicit hybrid time domain method for computational electromagnetics the numerical solution of maxwell s curl equations in the time domain is achieved by combining an unstructured mesh finite element algorithm with a cartesian finite difference method the practical problem area selected to illustrate the application of the approach is the simulation of three dimensional electromagnetic wave scattering the scattering obstacle and the free space region immediately adjacent to it are discretized using an unstructured mesh of linear tetrahedral elements the remainder of the computational domain is filled with a regular cartesian mesh these two meshes are overlapped to create a hybrid mesh for the numerical solution on the cartesian mesh an explicit finite difference method is adopted and an implicit explicit finite element formulation is employed on the unstructured mesh this approach ensures that computational efficiency is maintained if for any reason the generated unstructured mesh contains elements of a size much smaller than that required for accurate wave propagation a perfectly matched layer is added at the artificial far field boundary created by the truncation of the physical domain prior to the numerical solution the complete solution approach is parallelized to enable large scale simulations to be effectively performed examples are included to demonstrate the numerical performance that can be achieved