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introductory vibrations courses, Meirovitch offers a masterfully crafted textbook that covers all basic concepts at a level appropriate for undergraduate students. Scientific Computing, 2/e, presents a broad overview of numerical methods for solving all the major problems in scientific computing, including linear and nonlinear equations. An accessible(More)
The variational multiscale method is applied to the large eddy simulation ͑LES͒ of homogeneous, isotropic flows and compared with the classical Smagorinsky model, the dynamic Smagorinsky model, and direct numerical simulation ͑DNS͒ data. Overall, the multiscale method is in better agreement with the DNS data than both the Smagorinsky model and the dynamic(More)
A new mixed, stabilized, discontinuous Galerkin formulation for Darcy flow is presented. The formulation combines several attributes not simultaneously satisfied by other methods: It is convergent for any combination of velocity and pressure interpolation higher than first-order, it exactly satisfies a mass balance on each element, and it passes two-and(More)
We derive an explicit formula for the fine-scale Green's function arising in variational mul-tiscale analysis. The formula is expressed in terms of the classical Green's function and a projector which defines the decomposition of the solution into coarse and fine scales. The theory is presented in an abstract operator format and subsequently specialized for(More)
We consider a family of mixed finite element discretizations of the Darcy flow equations using totally discontinuous elements (both for the pressure and the flux variable). Instead of using a jump stabilization as it is usually done for DG methods (see e.g. [3], [13] and the references therein) we use the stabilization introduced in [18], [17]. We show that(More)
Current practice in vascular surgery utilizes only diagnostic and empirical data to plan treatments and does not enable quantitative a priori prediction of the outcomes of interventions. We have previously described a new approach to vascular surgery planning based on solving the governing equations of blood flow in patient-specific models. A(More)
We explore hierarchical refinement of NURBS as a basis for adaptive isogeometric and immersed boundary analysis. We use the principle of B-spline subdivision to derive a local refinement procedure , which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher(More)
This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a(More)