Thomas J. R. Hughes

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We propose a new class of Discontinuous Galerkin (DG) methods based on variational multiscale ideas. Our approach begins with an additive decomposition of the discontinuous finite element space into continuous (coarse) and discontinuous (fine) components. Variational multiscale analysis is used to define an interscale transfer operator that associates(More)
We describe an approach to construct hexahedral solid NURBS (Non-Uniform Rational B-Splines) meshes for patient-specific vascular geometric models from imaging data for use in isogeometric analysis. First, image processing techniques, such as contrast enhancement, filtering, classification, and segmentation, are used to improve the quality of the input(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)
This paper describes an approach to construct unstructured tetrahedral and hexa-hedral meshes for a domain with multiple materials. In earlier works, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a single-material domain. Based on this methodology, we introduce the notion of material change edge and use it to(More)
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Keywords: Trivariate solid T-spline Arbitrary genus topology Polycube Isogeometric analysis a b s t r a c t A comprehensive scheme is described to construct rational trivariate solid T-splines from boundary triangulations with arbitrary topology. To extract the topology of the input geometry, we first compute a smooth harmonic scalar field defined over the(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 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 study a multiscale discontinuous Galerkin method introduced in [10] that reduces the computational complexity of the discontinuous Galerkin method, seemingly without adversely affecting the quality of results. For a stabilized variant we are able to obtain the same error estimates for the advection-diffusion equation as for the usual discontinuous(More)