Domestic Arrangements: The Maid's Room in the Atakoy Apartment Blocks, Istanbul, Turkey

Cataloged from PDF version of article.The first phase of Istanbul's Ataköy Housing Development, an icon of architectural modernism in Turkey, inflects modernist architectural forms with local domestic traditions. This study examines the maid's room, a sphere of the Turkish modern interior where post-war ideas and ideals both reconciled and contradicted the customary and the modern. The case study extends recent attempts to re-think postwar architectural culture and its global effects

Accurate Solutions of Extremely Large Integral-Equation Problems in Computational Electromagnetics

Cataloged from PDF version of article.Accurate simulations of real-life electromagnetics problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be achieved easily, even when using the most powerful computers with state-of-the-art technology. However, with the multilevel fast multipole algorithm (MLFMA) and parallel MLFMA, we have been able to obtain full-wave solutions of scattering problems discretized with hundreds of millions of unknowns. Some of the complicated real-life problems (such as scattering from a realistic aircraft) involve geometries that are larger than 1000 wavelengths. Accurate solutions of such problems can be used as benchmarking data for many purposes and even as reference data for high-frequency techniques. Solutions of extremely large canonical benchmark problems involving sphere and National Aeronautics and Space Administration (NASA) Almond geometries are presented, in addition to the solution of complicated objects, such as the Flamme. The parallel implementation is also extended to solve very large dielectric problems, such as dielectric lenses and photonic crystals. © 1963-2012 IEEE

Hierarchical Parallelization of the Multilevel Fast Multipole Algorithm (MLFMA)

Cataloged from PDF version of article.Due to its O(NlogN) complexity, the multilevel fast multipole algorithm (MLFMA) is one of the most prized algorithms of computational electromagnetics and certain other disciplines. Various implementations of this algorithm have been used for rigorous solutions of large-scale scattering, radiation, and miscellaneous other electromagnetics problems involving 3-D objects with arbitrary geometries. Parallelization of MLFMA is crucial for solving real-life problems discretized with hundreds of millions of unknowns. This paper presents the hierarchical partitioning strategy, which provides a very efficient parallelization of MLFMA on distributed-memory architectures. We discuss the advantages of the hierarchical strategy over previous approaches and demonstrate the improved efficiency on scattering problems discretized with millions of unknowns

A Hierarchical Partitioning Strategy for an Efficient Parallelization of the Multilevel Fast Multipole Algorithm

Cataloged from PDF version of article.We present a novel hierarchical partitioning strategy for the efficient parallelization of the multilevel fast multipole algorithm (MLFMA) on distributed-memory architectures to solve large-scale problems in electromagnetics. Unlike previous parallelization techniques, the tree structure of MLFMA is distributed among processors by partitioning both clusters and samples of fields at each level. Due to the improved load-balancing, the hierarchical strategy offers a higher parallelization efficiency than previous approaches, especially when the number of processors is large. We demonstrate the improved efficiency on scattering problems discretized with millions of unknowns. In addition, we present the effectiveness of our algorithm by solving very large scattering problems involving a conducting sphere of radius 210 wavelengths and a complicated real-life target with a maximum dimension of 880 wavelengths. Both of the objects are discretized with more than 200 million unknowns

Contamination of the Accuracy of the Combined-Field Integral Equation with the Discretization Error of the Magnetic-Field Integral Equation

Cataloged from PDF version of article.We investigate the accuracy of the combined-field integral equation (CFIE) discretized with the Rao-Wilton-Glisson (RWG) basis functions for the solution of scattering and radiation problems involving three-dimensional conducting objects. Such a low-order discretization with the RWG functions renders the two components of CFIE, i.e., the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE), incompatible, mainly because of the excessive discretization error of MFIE. Solutions obtained with CFIE are contaminated with the MFIE inaccuracy, and CFIE is also incompatible with EFIE and MFIE. We show that, in an iterative solution, the minimization of the residual error for CFIE involves a breakpoint, where a further reduction of the residual error does not improve the solution in terms of compatibility with EFIE, which provides a more accurate reference solution. This breakpoint corresponds to the last useful iteration, where the accuracy of CFIE is saturated and a further reduction of the residual error is practically unnecessary

Singularity of the magnetic-field integral equation and its extraction

Cataloged from PDF version of article.In the solution of the magnetic-field integral equation (MFIE) by the method of moments (MOM) on planar triangulations, singularities arise both in the inner integrals on the basis functions and also in the outer integrals on the testing functions. A singularity-extraction method is introduced for the efficient and accurate computation of the outer integrals, similar to the way inner-integral singularities are handled. In addition, various formulations of the MFIE and the electric-field integral equation are compared, along with their associated restrictions

Enhancing the accuracy of the interpolations and Anterpolations in MLFMA

Cataloged from PDF version of article.We present an efficient technique to reduce the interpolation and anterpolation (transpose interpolation) errors in the aggregation and disaggregation processes of the multilevel fast multipole algorithm (MLFMA), which is based on the sampling of the radiated and incoming fields over all possible solid angles, i.e., all directions on the sphere. The fields sampled on the sphere are subject to various operations, such as interpolation, aggregation, translation, disaggregation, anterpolation, and integration. We identify the areas on the sphere, where the highest levels of interpolation errors are encountered. The error is reduced by employing additional samples on such parts of the sphere. Since the interpolation error is propagated and amplified by every level of aggregation, this technique is particulary useful for large problems. The additional costs in the memory and processing time are negligible, and the technique can easily be adapted into the existing implementations of MLFMA

Efficient Solution of the Electric-Field Integral Equation Using the Iterative LSQR Algorithm

Cataloged from PDF version of article.In this letter, we consider iterative solutions of the three-dimensional electromagnetic scattering problems formulated by surface integral equations. We show that solutions of the electric-field integral equation (EFIE) can be improved by employing an iterative least-squares QR (LSQR) algorithm. Compared to many other Krylov subspace methods, LSQR provides faster convergence and it becomes an alternative choice to the time-efficient no-restart generalized minimal residual (GMRES) algorithm that requires large amounts of memory. Improvements obtained with the LSQR algorithm become significant for the solution of large-scale problems involving open surfaces that must be formulated using EFIE, which leads to matrix equations that are usually difficult to solve iteratively, even when the matrix-vector multiplications are accelerated via the multilevel fast multipole algorithm

Discretization error due to the identity operator in surface integral equations

Cataloged from PDF version of article.We consider the accuracy of surface integral equations for the solution of scattering and radiation problems in electromagnetics. In numerical solutions, second-kind integral equations involving welltested identity operators are preferable for efficiency, because they produce diagonally-dominant matrix equations that can be solved easily with iterative methods. However, the existence of the well-tested identity operators leads to inaccurate results, especially when the equations are discretized with low-order basis functions, such as the Rao–Wilton–Glisson functions. By performing a computational experiment based on the nonradiating property of the tangential incident fields on arbitrary surfaces, we show that the discretization error of the identity operator is a major error source that contaminates the accuracy of the second-kind integral equations significantly. © 2009 Elsevier B.V. All rights reserve

The use of curl-conforming basis functions for the magnetic-field integral equation

Cataloged from PDF version of article.Divergence-conforming Rao-Wilton-Glisson (RWG) functions are commonly used in integral-equation formulations to model the surface current distributions on planar triangulations. In this paper, a novel implementation of the magnetic-field integral equation (MFIE) employing the curl-conforming (n) over tilde x RWG basis and testing functions is introduced for improved current modelling. Implementation details are outlined in the contexts of the method of moments, the fast multipole method, and the multilevel fast multipole algorithm. Based on the examples of electromagnetic modelling of conducting scatterers, it is demonstrated that significant improvement in the accuracy of the MFIE can be obtained by using the curl-conforming (n) over tilde x RWG functions