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334 results on '"Babuška, I."'

2. Stable Generalized Finite Element Method (SGFEM)

Author

Babuska, I. and Banerjee, U.

Subjects
Mathematics - Numerical Analysis
Abstract

The Generalized Finite Element Method (GFEM) is a Partition of Unity Method (PUM), where the trial space of standard Finite Element Method (FEM) is augmented with non-polynomial shape functions with compact support. These shape functions, which are also known as the enrichments, mimic the local behavior of the unknown solution of the underlying variational problem. GFEM has been successfully used to solve a variety of problems with complicated features and microstructure. However, the stiffness matrix of GFEM is badly conditioned (much worse compared to the standard FEM) and there could be a severe loss of accuracy in the computed solution of the associated linear system. In this paper, we address this issue and propose a modification of the GFEM, referred to as the Stable GFEM (SGFEM). We show that the conditioning of the stiffness matrix of SGFEM is not worse than that of the standard FEM. Moreover, SGFEM is very robust with respect to the parameters of the enrichments. We show these features of SGFEM on several examples., Comment: 51 pages, 4 figures

Published
2011
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10. Using Cyber-Infrastructure for Dynamic Data Driven Laser Treatment of Cancer

Author

Bajaj, C., Oden, J. T., Diller, K. R., Browne, J. C., Hazle, J., Babuška, I., Bass, J., Bidaut, L., Demkowicz, L., Elliott, A., Feng, Y., Fuentes, D., Kwon, B., Prudhomme, S., Stafford, R. J., Zhang, Y., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Rangan, C. Pandu, editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Shi, Yong, editor, van Albada, Geert Dick, editor, Dongarra, Jack, editor, and Sloot, Peter M. A., editor

Published
2007
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11. Development of a Computational Paradigm for Laser Treatment of Cancer

Author

Oden, J. T., Diller, K. R., Bajaj, C., Browne, J. C., Hazle, J., Babuška, I., Bass, J., Demkowicz, L., Feng, Y., Fuentes, D., Prudhomme, S., Rylander, M. N., Stafford, R. J., Zhang, Y., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Alexandrov, Vassil N., editor, van Albada, Geert Dick, editor, Sloot, Peter M. A., editor, and Dongarra, Jack, editor

Published
2006
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13. A Dynamic Data Driven Computational Infrastructure for Reliable Computer Simulations

Author

Oden, J. T., Browne, J. C., Babuška, I., Bajaj, C., Demkowicz, L. F., Gray, L., Bass, J., Feng, Y., Prudhomme, S., Nobile, F., Tempone, R., Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Bubak, Marian, editor, van Albada, Geert Dick, editor, Sloot, Peter M. A., editor, and Dongarra, Jack, editor

Published
2004
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