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pro vyhledávání: '"Aksoylu, Burak"'
Autor:
Aksoylu, Burak
Publikováno v:
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Thesis (Ph. D.)--University of California, San Diego, 2001.
Vita. Includes bibliographical references (leaves 137-140).
Vita. Includes bibliographical references (leaves 137-140).
Externí odkaz:
http://wwwlib.umi.com/cr/ucsd/fullcit?p3022190
Recent applications of machine learning, in particular deep learning, motivate the need to address the generalizability of the statistical inference approaches in physical sciences. In this letter, we introduce a modular physics guided machine learni
Externí odkaz:
http://arxiv.org/abs/2012.13343
Akademický článek
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We study nonlocal equations from the area of peridynamics on bounded domains. In our companion paper, we discover that, on $\mathbb{R}^n$, the governing operator in peridynamics, which involves a convolution, is a bounded function of the classical (l
Externí odkaz:
http://arxiv.org/abs/1411.3086
Publikováno v:
J. Math. Phys. 57, 062902 (2016)
We study equations from the area of peridynamics, which is an extension of elasticity. The governing equations form a system of nonlocal wave equations. Its governing operator is found to be a bounded, linear and self-adjoint operator on a Hilbert sp
Externí odkaz:
http://arxiv.org/abs/1409.7525
In this article, we develop goal-oriented error indicators to drive adaptive refinement algorithms for the Poisson-Boltzmann equation. Empirical results for the solvation free energy linear functional demonstrate that goal-oriented indicators are not
Externí odkaz:
http://arxiv.org/abs/1109.4092
Autor:
Aksoylu, Burak, Holst, Michael
Publikováno v:
SIAM J. Numer. Anal., Vol. 44 (2006), No. 3, pp. 1005-1025
In this article, we establish optimality of the Bramble-Pasciak-Xu (BPX) norm equivalence and optimality of the wavelet modified (or stabilized) hierarchical basis (WHB) preconditioner in the setting of local 3D mesh refinement. In the analysis of WH
Externí odkaz:
http://arxiv.org/abs/1001.1369
Publikováno v:
SIAM J. Sci. Comput., Vol. 25 (2003), No. 2, pp. 478-498
In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform refinement-based d
Externí odkaz:
http://arxiv.org/abs/1001.1370
Autor:
Aksoylu, Burak, Yeter, Zuhal
We study the high-contrast biharmonic plate equation with HCT and Morley discretizations. We construct a preconditioner that is robust with respect to contrast size and mesh size simultaneously based on the preconditioner proposed by Aksoylu et al. (
Externí odkaz:
http://arxiv.org/abs/0910.0487
Autor:
Aksoylu, Burak, Parks, Michael L.
In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems, proving a n
Externí odkaz:
http://arxiv.org/abs/0909.4504