Fast Mesh-based physical optics for large-scale electromagnetic analysis

Xiang, Daopu (2016-12)

Thesis (DPhil)--Stellenbosch University, 2016.

Thesis

ENGLISH ABSTRACT: At sufficiently high frequencies, the electrical size of scattering objects become very large. The electromagnetic field simulation of such objects becomes prohibitively expensive with physically rigorous (full wave) computational electromagnetics methods. In such cases, methods based on asymptotic assumptions can be employed instead, to approximately solve Maxwell’s equations. The physical optics (PO) approximation for a conducting surface, is a well-known asymptotic assumption. The multiple-reflection PO (MRPO) method is obtained by applying the PO approximation recursively, to model multiple reflections occurring internally to an object. The overall research goal of this work is to significantly accelerate the mesh-based MRPO for electromagnetic scattering analysis. A standard representation was chosen for the surface current, namely Rao- Wilton-Glisson (RWG) basis functions on a mesh of triangle elements. Since the MRPO is an extension of the single-reflection PO (SRPO), the main bottleneck in the SRPO, namely incident field shadowing determination, is addressed first. An adaptive, multilevel, buffer-based shadowing determination algorithm is developed which is robustly optimal, yielding O(N) time-scaling results for extreme test cases (N denotes the number of mesh elements). Secondly, the first ever, comprehensively accelerated version of the meshbased MRPO method (which rigorously takes internal shadowing into account), denoted fast MRPO (FMRPO), is developed. The FMRPO uses the multi-level, fast multipole method (MLFMM) to accelerate internal reflected field calculations. The inter-group interaction criterion of the MLFMM is altered to account for shadowing. Inter-group shadowing status flags are efficiently evaluated. The runtime scaling of the conventional MRPO is O(Nˆ2), while the runtime of the FMRPO scales as quasi-O(N log N), depending on the specific geometry. Results are presented for practical geometries with larger electrical sizes than have ever before been considered with the MRPO, but which can now for the first time be solved in realistically fast runtimes. With the FMRPO there is no fundamental limit to the electrical size of the scattering objects that can be solved.

AFRIKAANSE OPSOMMING: By genoegsaam hoë frekwensies is die elektriese grootte van verstrooiingsvoorwerpe baie groot. Die elektromagnetiese veldsimulasie van sulke voorwerpe met fisies omvattende (volgolf) numeriese elektromagnetika metodes word dan te duur. In sulke gevalle kan metodes gebaseer op asimptotiese aannames eerder ingespan word, om Maxwell se vergelykings by benadering op te los. Die fisiese optika (FO) benadering vir ’n geleidende oppervlak is ’n welbekende asimptotiese aanname. Die multi-refleksie FO (MRFO) metode word verkry deur die FO benadering rekursief toe te pas, om veelvoudige refleksies te modelleer wat intern tot ’n voorwerp plaasvind. Die hoof navorsingsdoelwit van hierdie werk is om die maas-gebaseerde MRFO noemenswaardig te versnel vir elektromagnetiese verstrooiingsanalise. ’n Standaard voorstelling is gekies vir die oppervlaktestroomdigtheid, naamlik Rao-Wilton-Glisson (RWG) basisfunksies op ’n maas van driehoek elemente. Gegee dat MRFO ’n uitbreiding van enkel-refleksie FO (ERFO) is, word die hoof bottelnek van die ERFO, naamlik invallende-veld skaduweebepaling, eerste aangespreek. ’n Aanpassingsvaardige, multivlak, buffer-gebaseerde, skaduweebepalingsalgoritme is ontwikkel wat robuust optimaal is, met O(N) tydskaleringsresultate vir uiterste toetsgevalle (N verwys na die aantal maaselemente). Tweedens is die heel eerste, omvattend versnelde weergawe van die maas-gebaseerde MRFO metode (wat interne skaduwees streng in ag neem), genoem vinnige MRFO (VMRFO), ontwikkel. Die VMRFO inkorporeer die multivlak, vinnige multipool metode (MVVMM) om interne, weerkaatste veldberekeninge te versnel. Die intergroep interaksiekriterium van die MVVMM is aangepas om skaduwees in ag te neem. Intergroep skadustatusvlaggies word doeltreffend bepaal. Die berekeningstyd van die konvensionele MRFO skaleer as O(Nˆ2), terwyl die berekeningstyd van die VMRFO skaleer as kwasi-O(N log N), na gelang van die spesifieke geometrie. Resultate word getoon vir praktiese verstrooiingsvoorwerpe wat elektries groter is as wat ooit vantevore met die MRFO aangepak is, wat nou vir die eerste keer opgelos kan word in realisties vinnige berekeningstye. Met die VMRFO is daar geen fundamentele beperking op die elektriese grootte van die verstrooiingsvoorwerpe wat kan opgelos word nie.

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