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Author

Y. Krongauz

Bio: Y. Krongauz is an academic researcher from Northwestern University. The author has contributed to research in topics: Galerkin method & Meshfree methods. The author has an hindex of 8, co-authored 8 publications receiving 4399 citations.

Papers
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Journal ArticleDOI
Ted Belytschko1, Y. Krongauz1, D. Organ1, Mark Fleming1, Petr Krysl1 
TL;DR: Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined and it is shown that the three methods are in most cases identical except for the important fact that partitions ofunity enable p-adaptivity to be achieved.

3,082 citations

Journal ArticleDOI
TL;DR: In this article, a procedure for coupling meshless methods such as the element-free Galerkin method with finite element methods is developed so that continuity and consistency are preserved on the interface elements.
Abstract: A procedure is developed for coupling meshless methods such as the element-free Galerkin method with finite element methods. The coupling is developed so that continuity and consistency are preserved on the interface elements. Results are presented for both elastostatic and elastodynamic problems, including a problem with crack growth.

452 citations

Journal ArticleDOI
TL;DR: The technique employs a string of elements along the essential boundaries and combines the finite element shape functions with the approximation, and the resulting approximation can exactly reproduce linear polynomials so that it satisfies the patch test.

343 citations

Journal ArticleDOI
TL;DR: Numerical results show that approximations which do not satisfy the completeness and integrability conditions fail to converge for linear elastostatics, so convergence is not expected in nonlinear continuum mechanics.
Abstract: The completeness of smoothed particle hydrodynamics (SPH) and its modiications is investigated. Completeness, or the reproducing conditions, in Galerkin approximations play the same role as consistency in nite diierence approximations. Several techniques which restore various levels of completeness by satisfying reproducing conditions on the approximation or the derivatives of the approximation are examined. A Petrov-Galerkin formulation for a particle method is developed using approximations with corrected derivatives. It is compared to a normalized SPH formulation based on kernel approximations and a Galerkin method based on moving least square approximations. It is shown that the major diierence is that in the SPH discretization the function which plays the role of the test function is not integrable. Numerical results show that approximations which do not satisfy the completeness and integrability conditions fail to converge for linear elastostatics, so convergence is not expected in nonlinear continuum mechanics.

281 citations

Journal ArticleDOI
TL;DR: In this article, a technique for incorporating discontinuities in derivatives into meshless methods is presented, which enriches the approximation by adding special shape functions that contain discontinuity in derivatives.
Abstract: A technique for incorporating discontinuities in derivatives into meshless methods is presented. The technique enriches the approximation by adding special shape functions that contain discontinuities in derivatives. The special shape functions have compact support which results in banded matrix equations. The technique is described in element-free Galerkin context, but is easily applicable to other meshless methods and projections. Numerical results for problems in one and two dimensions are reported. © 1998 John Wiley & Sons, Ltd.

179 citations


Cited by
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Journal ArticleDOI
TL;DR: In this article, a minimal remeshing finite element method for crack growth is presented, where Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack.
Abstract: A minimal remeshing finite element method for crack growth is presented. Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack. This method allows the crack to be arbitrarily aligned within the mesh. For severely curved cracks, remeshing may be needed but only away from the crack tip where remeshing is much easier. Results are presented for a wide range of two-dimensional crack problems showing excellent accuracy. Copyright © 1999 John Wiley & Sons, Ltd.

4,185 citations

Journal ArticleDOI
TL;DR: In this article, the theory and application of Smoothed particle hydrodynamics (SPH) since its inception in 1977 are discussed, focusing on the strengths and weaknesses, the analogy with particle dynamics and the numerous areas where SPH has been successfully applied.
Abstract: In this review the theory and application of Smoothed particle hydrodynamics (SPH) since its inception in 1977 are discussed. Emphasis is placed on the strengths and weaknesses, the analogy with particle dynamics and the numerous areas where SPH has been successfully applied.

4,070 citations

Journal ArticleDOI
Ted Belytschko1, Y. Krongauz1, D. Organ1, Mark Fleming1, Petr Krysl1 
TL;DR: Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined and it is shown that the three methods are in most cases identical except for the important fact that partitions ofunity enable p-adaptivity to be achieved.

3,082 citations

Journal ArticleDOI
TL;DR: An overview on the SPH method and its recent developments is presented, including the need for meshfree particle methods, and advantages of SPH, and several important numerical aspects.
Abstract: Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

1,398 citations

Journal ArticleDOI
TL;DR: In this article, an implementation of the smoothed particle hydrodynamics (SPH) method is presented to treat two-dimensional interfacial flows, that is, flow fields with different fluids separated by sharp interfaces.

1,319 citations