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The mentor will meet with the mentee) Tj 0.00 -18.00 Td (twice a semester to check in on progress and offer outside) Tj 0.00 -18.00 Td (guidance but additional meetings can be added if needed. ) Tj ET Q EMC endstream endobj 28 0 obj <> /Font <> >> /F 4 /FT /Tx /Ff 4096 /P 1 0 R /Rect [74.04 178.68 557.52 283.44 ] /Subtype /Widget /T (Level of research per semester) /TU (have 100% research allocation, whereas a TA would have 50) /Type /Annot /V (50% research effort in AY09/10, and 100% research effort in AY10/11 ) /AP <> >> endobj 39 0 obj <> /Font <> >> /F 4 /FT /Tx /Ff 4096 /P 1 0 R /Rect [74.04 438.84 557.52 554.88 ] /Subtype /Widget /T (Dissemination) /TU (research visits, etc) /Type /Annot /V (The candidate will submit papers to journals such as the Journal of Computational Physics and will give talks at conferences. Conferences to be attended include SIAM CSE, ICIAM, SIAM Annual, and SIAM Numerical Linear Algebra. 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The planned research will make use of potential) Tj 0.00 -17.00 Td (theory and randomized linear algebra to efficicently form low) Tj 0.00 -17.00 Td (rank factorizations needed for a hierarchical factorization of the) Tj 0.00 -17.00 Td (dense matrices of interest. A variant of the Sherman-Morrison) Tj 0.00 -17.00 Td (formula will be developed to create an approximation of the) Tj 0.00 -17.00 Td (inverse. The resulting methods will be applied to discretized) Tj 0.00 -17.00 Td (integral equations for elliptic and Helmholtz problems and to) Tj 0.00 -17.00 Td (accelerate sparse solvers for finite element discretizations. ) Tj ET Q EMC endstream endobj 70 0 obj <> /Font <> >> /F 4 /FT /Tx /Ff 4096 /P 48 0 R /Rect [74.04 200.52 557.52 390 ] /Subtype /Widget /T (Research description) /TU (Brief description of the research to be performed) /Type /Annot /V (Develop linear scaling direct solvers for the linear systems that arise from the discretization of elliptic partial differential equations. The planned research will make use of potential theory and randomized linear algebra to efficicently form low rank factorizations needed for a hierarchical factorization of the dense matrices of interest. A variant of the Sherman-Morrison formula will be developed to create an approximation of the inverse. 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