On the accuracy of the Adaptive Cross Approximation algorithm

This contribution identifies an often ignored source of uncertainty in the accuracy of the Adaptive Cross Approximation (ACA) algorithm.Postprint (published version

Error bound of the multilevel adaptive cross approximation (MLACA)

An error bound of the multilevel adaptive cross approximation (MLACA 1, which is a multilevel version of the adaptive cross approximation-singular value decomposition (ACA-SVD), is rigorously derived. For compressing an off-diagonal submatrix of the method of moments MAD impedance matrix with a binary tree, the L-level MIACA includes L + 1 steps, and each step includes 2(L) ACA-SVD decompositions. If the relative Frobenius norm error of the ACA-SVD used in the MLACA is smaller than epsilon, the rigorous proof in this communication shows that the relative Frobenius norm error of the L-Ievel MLACA is smaller than (1 + epsilon)(L+1) - 1. In practical applications, the error bound of the MLACA can be approximated as epsilon(L + 1), because epsilon is always << 1. The error upper bound can he used to control the accuracy of the MLACA. To ensure an error of the L-level MLACA smaller than epsilon for different L, the ACA-SVD threshold can be set to (1 + epsilon)1/L+1 - 1, which approximately equals epsilon/(L + 1) for practical applications.Peer ReviewedPostprint (author's final draft

Tangential-normal surface testing for the nonconforming discretization of the electric-field integral equation

©2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Nonconforming implementations of the electric-field integral equation (EFIE), based on the facet-oriented monopolar-RWG set, impose no continuity constraints in the expansion of the current between adjacent facets. These schemes become more versatile than the traditional edge-oriented schemes, based on the RWG set, because they simplify the management of junctions in composite objects and allow the analysis of nonconformal triangulations. Moreover, for closed moderately small conductors with edges and corners, they show improved accuracy with respect to the conventional RWG-discretization. However, they lead to elaborate numerical schemes because the fields are tested inside the body, near the boundary surface, over volumetric subdomains attached to the surface meshing. In this letter, we present a new nonconforming discretization of the EFIE that results from testing with RWG functions over pairs of triangles such that one triangle matches one facet of the surface triangulation and the other one is oriented perpendicularly, inside the body. This “tangential-normal” testing scheme, based on surface integrals, simplifies considerably the matrix generation when compared to the volumetrically tested approaches.Peer ReviewedPostprint (author's final draft

Analysis of microstrip antennas by multilevel matrix decomposition algorithm

Integral equation methods (IE) are widely used in conjunction with Method of Moments (MoM) discretization for the numerical analysis of microstrip antennas. However, their application to large antenna arrays is difficult due to the fact that the computational requirements increase rapidly with the number of unknowns N. Several techniques have been proposed to reduce the computational cost of IE-MoM. The Multilevel Matrix Decomposition Algorithm (MLMDA) has been implemented in 3D for arbitrary perfectly conducting surfaces discretized in Rao, Wilton and Glisson linear triangle basis functions . This algorithm requires an operation count that is proportional to N·log2N. The performance of the algorithm is much better for planar or piece-wise planar objects than for general 3D problems, which makes the algorithm particularly well-suited for the analysis of microstrip antennas. The memory requirements are proportional to N·logN and very low. The main advantage of the MLMDA compared with other efficient techniques to solve integral equations is that it does not rely on specific mathematical properties of the Green's functions being used. Thus, we can apply the method to interesting configurations governed by special Green's functions like multilayered media. In fact, the MDA-MLMDA method can be used at the top of any existing MoM code. In this paper we present the application to the analysis of large printed antenna arrays.Peer ReviewedPostprint (published version

Incomplete Letters from 0. G.Heldring to Professor Harting on Theological and Scientific Matters

These two items are incomplete letters from O. G. Heldring to Professor Harting on theological and scientific matters.https://digitalcommons.hope.edu/vrp_1860s/1058/thumbnail.jp

State Capacity and Violence: Evidence from the Rwandan Genocide

Abstract Exploiting local variation in state capacity within Rwanda I investigate the link between state capacity and violence. Using a disaggregated measure of the intensity of the 1994 Rwandan genocide, I establish that greater local state capacity led to greater conflict intensity. I proxy modern state capacity with its precolonial counterpart, measured by the total time a district was incorporated in the precolonial kingdom. This &apos;duration of incorporation&apos; measures the cumulative effect of the centralizing forces in the kingdom and acts as a proxy for state capacity. Since the kingdom expanded through conquest and consolidated through patronage relations revolving around cattle, I instrument the duration of incorporation with the geographical suitability for cattle. This strategy establishes a causal interpretation of the main result. State capacity, while usually associated with greater public good provision and higher GDP, played a central role in the mass killings in Rwanda

Integrating cellular and tissue dynamics with cell fate decisions through computational modeling

There is a need for alternative methods to replace, reduce and refine (3R) animal experimentation. Combining experimental data from high-throughput in vitro studies with in silico modeling is a promising approach to unravel the effect of chemicals on living cells and to gain a better understanding of the processes leading to adverse effects. Exposure to chemicals can activate various stress response pathways that limit the amount of cellular damage, help cells to recover or orchestrate irreversible cell fates such as apoptosis. In this thesis, we use experimental data and current knowledge on stress pathway activation and cell fate to create different types of computational models. With these models, we mathematically describe intracellular protein signaling cascades activated upon exposure to various compounds and their link to cell fate. In this way, we integrate molecular-level biological processes to cell-level phenomena such as cell cycle progression, senescence and necrosis, and generate new hypotheses about the mechanisms underlying adversity.Toxicolog

GRECO: 30 years of graphical processing techniques for RCS computation

This contribution to the special session in honor of Prof. Rafael Gómez-Martín will address the 30 year development of graphical processing techniques (GRECO) for fast computation of Radar Cross Section (RCS) of electrically large and complex targets. The development of GRECO started in 1988, in the frame of the “Applied research project for the development and validation of numerical methods for RCS prediction, analysis and optimization”, in which I had the pleasure to know Rafael since our groups where participating together in the project. The development of GRECO never stopped, and recently it has been updated by replacing the graphical processing technique for computation of surface reflection and edge diffraction by a hybrid CPU-graphical processing approach. The resulting code has the same accuracy as conventional RCS computation techniques, but detection of shadowed surfaces and edges is one order of magnitude faster than the most efficient O(N logN) implementations.Peer ReviewedPostprint (published version

Fast direct solution of method of moments applied to multiscale problems

In a recent publication [1], we proposed a new convergence criterion for the Adapted Cross Approximation (ACA) algorithm, based on random sampling of the matrix that represents the residual error at each step of the algorithm. We presented some practical examples involving RCS computations of perfectly conducting benchmark targets exhibiting multiscale features, meaning that the mesh-size of the discrete model of the target is highly variable. These examples demonstrated a considerable improvement in the accuracy of the RCS result without appreciable loss of efficiency. In the presented examples, the solution was obtained by an iterative solver applied to an ACA-compressed Method of Moments impedance matrix. In this paper we apply the new method from [1] to the direct (non-iterative) solution of the MoM matrix. The results demonstrate that in this case, the advantage of the new method is far more important. Compared to ordinary ACA, the same accuracy is obtained in less than a quarter of the computation time