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Tj ET Q EMC endstream endobj 66 0 obj <> /Font <> >> /F 4 /FT /Tx /P 48 0 R /Rect [179.88 560.52 528.6 588.72 ] /Subtype /Widget /T (Name) /TU (undefined) /Type /Annot /V (þÿAdrianna Gillman) /AP <> >> endobj 67 0 obj <> /Font <> >> /F 4 /FT /Tx /P 48 0 R /Rect [179.88 531.48 528.6 559.68 ] /Subtype /Widget /T (Dissertation advisor) /TU (Dissertation advisor) /Type /Annot /V (þÿPer-Gunnar Martinsson) /AP <> >> endobj 68 0 obj <> /Font <> >> /F 4 /FT /Tx /P 48 0 R /Rect [179.88 502.2 528.6 530.4 ] /Subtype /Widget /T (Faculty mentor) /TU (Faculty mentor) /Type /Annot /V (þÿGregory Beylkin) /AP <> >> endobj 69 0 obj <> /Font <> >> /F 4 /FT /Tx /Ff 4096 /P 48 0 R /Rect [74.04 422.28 557.52 468 ] /Subtype /Widget /T (Draft dissertation title) /TU (Draft dissertation title) /Type /Annot /V (þÿFast direct solvers for elliptic partial differential equations) /AP <> >> 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 (þÿDevelop linear scaling direct solvers for the linear systems that arise from the discretization of elliptic partial differential equations.) /AP <> >> endobj 83 0 obj <> stream ÿÿŸL w¢*¤j¦Å¨iªõ­ì± ²-³?´Kµ–·W¸Ž¹ê»,¼ê¿U endstream endobj startxref 48981 %%EOF 8 2 obj <> /Font <> >> >> stream /Tx BMC q BT /Helv 20.00 Tf 0 g 1 0 0 1 0 101.76 Tm 2.00 -20.00 Td (50% research effort in AY09/10, and 100% research) Tj 0.00 -20.00 Td (effort in AY10/11) Tj ET Q EMC endstream endobj 13 2 obj <> /Font <> >> >> stream /Tx BMC q BT /Helv 17.00 Tf 0 g 1 0 0 1 0 113.04 Tm 2.00 -17.00 Td (The candidate will submit papers to journals such as the) Tj 0.00 -17.00 Td (Journal of Computational Physics and will give talks at) Tj 0.00 -17.00 Td (conferences. Conferences to be attended include SIAM CSE,) Tj 0.00 -17.00 Td (ICIAM, SIAM Annual, and SIAM Numerical Linear Algebra. ) Tj 0.00 -17.00 Td (The first paper should be submitted to the Journal of) Tj 0.00 -17.00 Td (Computational Physics by the begining of the fourth year.) Tj ET Q EMC endstream endobj 14 2 obj <> /Font <> >> >> stream /Tx BMC q BT /Helv 18.00 Tf 0 g 1 0 0 1 0 113.04 Tm 2.00 -18.00 Td (Advisor will meet with mentee once a week but will be) Tj 0.00 -18.00 Td (available for question via email and can arrange additional) Tj 0.00 -18.00 Td (meetings if needed. 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 (þÿ50% 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 (þÿThe 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. The first paper should be submitted to the Journal of Computational Physics by the begining of the fourth year. ) /AP <> >> endobj 40 0 obj <> /Font <> >> /F 4 /FT /Tx /Ff 4096 /P 1 0 R /Rect [74.04 601.8 557.52 717.84 ] /Subtype /Widget /T (Advisor and mentor commitments) /TU (undefined) /Type /Annot /V (þÿAdvisor will meet with mentee once a week but will be available for question via email and can arrange additional meetings if needed. The mentor will meet with the mentee twice a semester to check in on progress and offer outside guidance but additional meetings can be added if needed. ) /AP <> >> endobj 53 2 obj <> /Font <> >> >> stream /Tx BMC q BT /Helv 17.00 Tf 0 g 1 0 0 1 0 186.48 Tm 2.00 -17.00 Td (Develop linear scaling direct solvers for the linear systems that) Tj 0.00 -17.00 Td (arise from the discretization of elliptic partial differential) Tj 0.00 -17.00 Td (equations. 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 (þÿDevelop 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. The resulting methods will be applied to discretized integral equations for elliptic and Helmholtz problems and to accelerate sparse solvers for finite element discretizations. ) /AP <> >> endobj 84 0 obj <> stream ÿÿÀßÂCÅdžÉvÍQÐÉÔÿÛ> endstream endobj startxref 56126 %%EOF