We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in discretizations of H(div) spaces and Nedelec elements in discretizations of H(curl) spaces. We explain vectorization ideas and comment on a freely available MATLAB code which is fast and scalable with respect to time.Comment: 12 pages, 5 figures, ESCO 2014 conferenc

In this paper we present a simple method of deriving a posteriori error equalities and estimates for linear elliptic and parabolic partial differential equations. The error is measured in a combined norm taking into account both the primal and dual variables. We work only on the continuous (often called functional) level and do not suppose any specific properties of numerical methods and discretizations.Date: October 25, 2018. 1991 Mathematics Subject Classification. 65N15.

Abstract. We present an algorithm for two-and three-dimensional capacitance analysis on multidielectric integrated circuits of arbitrary geometry. Our algorithm is stochastic in nature and as such fully parallelizable. It is intended to extract capacitance entries directly from a pixelized representation of the integrated circuit (IC), which can be produced from a scanning electron microscopy image. Preprocessing and monitoring of the capacitance calculation are kept to a minimum, thanks to the use of distance maps automatically generated with a fast marching technique. Numerical validation of the algorithm shows that the systematic error of the algorithm decreases with better resolution of the input image. Those features render the presented algorithm well suited for fast prototyping while using the most realistic IC geometry data.

In this short note we consider several widely used L 2 -orthogonal Helmholtz decompositions for bounded domains in R 3 . It is well known that one part of the decompositions is a subspace of the space of functions with zero mean. We refine this global property into a local equivalent: we show that functions from these spaces have zero mean in every subdomain of specific decompositions of the domain.An application of the zero mean properties is presented for convex domains. We introduce a specialized Poincaré-type inequality, and estimate the related unknown constant from above. The upper bound is derived using the upper bound for the Poincaré constant proven by Payne and Weinberger. This is then used to obtain a small improvement of upper bounds of two Maxwell-type constants originally proven by Pauly.Although the two dimensional case is not considered, all derived results can be repeated in R 2 by similar calculations.

-In this paper, we discuss a posteriori estimates for the Maxwell type boundary-value problem. The estimates are derived by transformations of integral identities that define the generalized solution and are valid for any conforming approximation of the exact solution. It is proved analytically and confirmed numerically that the estimates indeed provide a computable and guaranteed bound of approximation errors. Also, it is shown that the estimates imply robust error indicators that represent the distribution of local (inter-element) errors measured in terms of different norms.