Abstract-Efficient functional derivative formulas suitable for optimal discretization based refinement criteria are developed for 3-D adaptive finite element analysis (FEA) with vector tetrahedra. Results for generalized vector Helmholtz systems are derived directly from first principles, and confirmed numerically through fundamental benchmark evaluations. Practical adaption applications are illustrated for selected FEA refinement models.Index Terms-Adaptive systems, electromagnetic analysis, error analysis, finite element methods.
-One of the major research issues in adaptive finite element analysis is the feedback control system used to guide the adaption. Essentially, one needs to resolve which error data to feedback after each iteration, and how to use it to initialize the next adaptive step. Variational aspects of optimal discretizations for scalar Poisson and Helmholtz systems are used to derive new refinement criteria for adaptive finite element solvers. They are shown to be effective and economical for h-,p-and hp-schemes.
In this paper, a mixed Finite-Element Time-Domain (FETD) method is presented for the simulation of electrically complex materials, including general combinations of linear dispersion, instantaneous nonlinearity, and dispersive nonlinearity. Using both edge and face elements, the presented method offers greater geometric flexibility than existing Finite-Difference Time-Domain (FDTD) implementations, and in contrast to existing nonlinear FETD methods, also incorporates both linear and nonlinear material dispersion. Dielectric nonlinearity is incorporated into the Crank-Nicolson mixed FETD formulation via a straightforward Newton-Raphson approach, for which the associated Jacobian is derived. Moreover, the dispersion is modeled via the Möbius z-transform method, yielding a simpler more general algorithm. The method's accuracy and convergence are verified, and its capability demonstrated via the simulation of several nonlinear phenomena, including temporal and spatial solitons in two spatial dimensions.
A wide class of finite-element (FE) electromagnetic applications requires computing very large sparse matrix vector multiplications (SMVM). Due to the sparsity pattern and size of the matrices, solvers can run relatively slowly. The rapid evolution of graphic processing units (GPUs) in performance, architecture, and programmability make them very attractive platforms for accelerating computationally intensive kernels such as SMVM. This work presents a new algorithm to accelerate the performance of the SMVM kernel on graphic processing units.Index Terms-Computer architecture, graphic processing units (GPUs), parallel processing, sparse matrix vector multiplication (SMVM).
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