A domain decomposition scheme based on the equivalence theorem and the method of moments is introduced. The unknowns on every subscatterer are transferred to the unknowns on its surrounding equivalent surface. With this scheme, both the number of unknowns and the memory usage are reduced. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1853–1857, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21777

A domain decomposition scheme based on the equivalence principle, also known as Huygens' principle, for integral equation solvers and the method of moments is introduced here. The equivalence principle allows the replacement of unknown currents distributed in a volume in space by equivalent currents residing on the surface that bounds the volume. In this manner, a problem of high complexity can be replaced by a surface of simpler shape. A tap basis is introduced to model the current that intercepts with the equivalence surfaces. Using this scheme, the current continuity is conserved and the singularity of the charges is avoided. The solution is shown to be accurate. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 2218–2222, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21933

Abstract-A method for calculating the Casimir force between large, complex 3D objects is presented. Difficulties have previously arisen in broadband multiscale calculation using CEM methods. To expand the range of problems that can be calculated, we use an integral equation, domain decomposition method (DDM) and argument principle to derive the Casimir force formula. The broadband integral equation DDM, which is the augmented equivalence principle algorithm (A-EPA), allows for an efficient broadband solution of large, complex objects. A-EPA subdivides a complex problem into separate smaller subproblems that are later recombined into a reduced matrix. This yields a reduced number of unknowns for complex structures making them feasible with modest computer resources. We demonstrate the advantages of the A-EPA by simulating large, finite, 3D, unaligned corrugated plates, which have previously only been modeled approximately as infinite plates using 2D techniques.

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