h goal of k work performed under this gram hasbeen CO develop high-qtxvlitytools for Sinndaung compkix systems that are represented by sohhs to partialdiffererltid equ8tims Examples include the simulation of combustion dcviccs and Ofv~ous kinds Ofrk ufaeturing pr~ses. Soch systems are chammxizd by dw pres=ce of multiple physical processes, of complex geometries, and of muhiple kngth and time scales. 'k this end, we iicvclopid a m,amlxxOfnew methodstha[ aft required to simulate a variety of

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... ex systems.~fichxk methods for~m~@ pr~blems with muhiple~Q%M, WXIXIUC and robust finite diffitretu discmxizalio~mehods fw adaptively concentrating coqutaticml effor% whereiris most iwedea and general, kxib]c merhods for representing complex gcometdes.