Trillion CellCAD BasedCartesian MeshGeneration fortheFinite Difference TimeDomainMethod on a4Gigabyte LinuxWorkstation

A robust, CAD based, highly accurate andfast Cartesian meshgeneration technique foracolossal numberof cells capacity usinga minimalsingle processor computing resource ispresented. Thecells aregenerated inYeeformat for theFinite Difference TimeDomainmethod.Therearethree key techniques presented thatachieve thiscapability: a memory efficient raytracing method,a highlyaccurate ray-facet intersection test, anda novelexactarithmetic tie-breaking algorithm forraysintersecting facet edges andvertices. IndexTerms-FDTD methods, finite difference methods, mesh generation. I.INTRODUCTION TheAirForce Research Laboratory (AFRL)atKirtland Air ForceBaseNew Mexico, United States, hasdeveloped a highlyaccurate androbustcubiccellmeshgenerator "Cubegen" capable oftrillion pluscell meshesona single processor Linuxboxwithonly4Gigabytes ofmainmemory. Inaddition, AFRL hasalsodeveloped aFinite Difference TimeDomain(FDTD)code"TMax"that easily andefficiently harnesses thousands ofprocessors. Combinedwithever increasing processor speeds, memorysizeandnumberof processors, large volumes withhighresolution areeasily modeled yielding a powerful timedomainelectromagnetic simulation tool. Unlike unstructured codes withCADbased meshgeneration tools, FDTD modelers oftenbuildmeshesusingtime consuming andcumbersome methods. However, Srisukh etal (1)demonstrated thata raytracing methodcanbe implemented on surface facetfiles generated by CAD software yielding acubic cell YeemeshforFDTD.Srisukh doesnotmentiontheefficient memoryusageofthis algorithm, allowing foramassive numberofcells withonlya minimal amountofcomputer memory.By employing a Boolean operation facet-ray intersection testusedbythe computational fluid mechanics community (2), andanovel exactarithmetic tie-breaker algorithm forrayintersections on facet edges andvertices, ahighly robust, fast andaccurate meshgeneration codecanbedeveloped.