Author
John E. Dolbow
Other affiliations: Northwestern University, University of New Hampshire
Bio: John E. Dolbow is an academic researcher from Duke University. The author has contributed to research in topics: Finite element method & Extended finite element method. The author has an hindex of 37, co-authored 79 publications receiving 11876 citations. Previous affiliations of John E. Dolbow include Northwestern University & University of New Hampshire.
Papers published on a yearly basis
Papers
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TL;DR: In this article, a displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method.
Abstract: SUMMARY An improvement of a new technique for modelling cracks in the nite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique. Copyright ? 1999 John Wiley & Sons, Ltd.
5,815 citations
TL;DR: In this paper, a new technique for the finite element modeling of cracks with multiple branches, multiple holes and cracks emanating from holes is presented, which allows the representation of crack discontinuities and voids independently of the mesh.
Abstract: SUMMARY Extensions of a new technique for the nite element modelling of cracks with multiple branches, multiple holes and cracks emanating from holes are presented. This extended nite element method (X-FEM) allows the representation of crack discontinuities and voids independently of the mesh. A standard displacementbased approximation is enriched by incorporating discontinuous elds through a partition of unity method. A methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed. Computation of the stress intensity factors (SIF) in dierent examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique. Copyright ? 2000 John Wiley & Sons, Ltd.
943 citations
TL;DR: In this paper, the eXtended Finite Element Method (X-FEM) is used to discretize the equations, allowing for the modeling of cracks whose geometry is independent of the finite element mesh.
546 citations
TL;DR: An approximate analytical method is presented to evaluate efficiently and accurately the call blocking probabilities in wavelength routing networks with multiple classes of calls, and path decomposition algorithms for single-class wavelength routing Networks may be readilt extended to the multiclass case.
411 citations
TL;DR: The character of the shape functions in meshfree methods is reviewed and compared to those used in the Finite Element Method and a construct for integration cells which reduces quadrature error is presented.
Abstract: The numerical integration of Galerkin weak forms for meshfree methods is investigated and some improvements are presented. The character of the shape functions in meshfree methods is reviewed and compared to those used in the Finite Element Method (FEM). Emphasis is placed on the relationship between the supports of the shape functions and the subdomains used to integrate the discrete equations. The construction of quadrature cells without regard to the local supports of the shape functions is shown to result in the possibility of considerable integration error. Numerical studies using the meshfree Element Free Galerkin (EFG) method illustrate the effect of these errors on solutions to elliptic problems. A construct for integration cells which reduces quadrature error is presented. The observations and conclusions apply to all Galerkin methods which use meshfree approximations.
390 citations
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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
Book•
24 Feb 2012
TL;DR: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software.
Abstract: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
2,372 citations
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
TL;DR: In this article, an extended finite element method is applied to modeling growth of arbitrary cohesive cracks, which is governed by requiring the stress intensity factors at the tip of the cohesive zone to vanish.
1,395 citations
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