Thomas J. R. Hughes

University of Texas at Austin

AlgorithmPhysicsMathematical optimizationMathematical analysisFinite element methodMixed finite element methodNonlinear systemComputational fluid dynamicsBoundary value problemGalerkin methodExtended finite element methodGeometryIsogeometric analysisApplied mathematicsMathematicsComputer scienceNumerical analysisMechanicsDiscretizationClassical mechanics

490Publications

152H-index

72.6kCitations

Publications 466

Removal of spurious outlier frequencies and modes from isogeometric discretizations of second- and fourth-order problems in one, two, and three dimensions

#1René R. Hiemstra (Leibniz University of Hanover)H-Index: 10

#2Thomas J. R. Hughes (University of Texas at Austin)H-Index: 152

Last. Dominik Schillinger (Leibniz University of Hanover)H-Index: 25

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Abstract null null null null A key advantage of isogeometric null discretizations null null is their accurate and well-behaved null eigenfrequencies null and null null null eigenmodes . For degree two and higher, however, a few spurious modes appear that possess inaccurate frequencies, denoted as “outliers”. The outlier frequencies and corresponding modes are at the root of several efficiency and robustness issues in isogeometric analysis. One example is explicit dynamics where outlier frequenci...

Galerkin formulations of isogeometric shell analysis: Alleviating locking with Greville quadratures and higher-order elements

#1Zhihui Zou (University of Texas at Austin)H-Index: 7

#2Thomas J. R. Hughes (University of Texas at Austin)H-Index: 152

Last. E.J. Savitha (RWTH Aachen University)H-Index: 1

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Abstract We propose new quadrature schemes that asymptotically require only four in-plane points for Reissner–Mindlin shell elements and nine in-plane points for Kirchhoff–Love shell elements in B-spline and NURBS-based isogeometric shell analysis, independent of the polynomial degree p of the elements. The quadrature points are Greville abscissae associated with p th-order B-spline basis functions whose continuities depend on the specific Galerkin formulations , and the quadrature weights are c...

Patient specific, imaging-informed modeling of rhenium-186 nanoliposome delivery via convection-enhanced delivery in glioblastoma multiforme.

#1Ryan T. WoodallH-Index: 3

#2David A. HormuthH-Index: 15

Last. Thomas E. YankeelovH-Index: 52

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Convection-enhanced delivery of rhenium-186 (186Re)-nanoliposomes is a promising approach to provide precise delivery of large localized doses of radiation for patients with recurrent glioblastoma multiforme. Current approaches for treatment planning utilizing convection-enhanced delivery are designed for small molecule drugs and not for larger particles such as186Re-nanoliposomes. To enable the treatment planning for186Re-nanoliposomes delivery, we have developed a computational fluid dynamics ...

#1Xiaodong Wei (EPFL: École Polytechnique Fédérale de Lausanne)H-Index: 10

#2Xin Li (USTC: University of Science and Technology of China)H-Index: 61

Last. Thomas J. R. Hughes (University of Texas at Austin)H-Index: 152

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This paper presents an enhanced version of our previous work, hybrid non-uniform subdivision surfaces [19], to achieve optimal convergence rates in isogeometric analysis. We introduce a parameter \lambda(\frac{1}{4}<\lambda<1 to control the rate of shrinkage of irregular regions, so the method is called tuned hybrid non-uniform subdivision (tHNUS). Our previous work corresponds to the case when \lambda=\frac{1}{2} While introducing \lambdain hybrid subdivision significantly complicat...

Isogeometric discrete differential forms : Non-uniform degrees, Bézier extraction, polar splines and flows on surfaces

#1Deepesh Toshniwal (TU Delft: Delft University of Technology)H-Index: 8

#2Thomas J. R. Hughes (University of Texas at Austin)H-Index: 152

Abstract Spaces of discrete differential forms can be applied to numerically solve the partial differential equations that govern phenomena such as electromagnetics and fluid mechanics. Robustness of the resulting numerical methods is complemented by pointwise satisfaction of conservation laws (e.g., mass conservation) in the discrete setting. Here we present the construction of isogeometric discrete differential forms, i.e., differential form spaces built using smooth splines. We first present ...

#1Xiaodong WeiH-Index: 10

#2Xin LiH-Index: 61

Last. Hugo CasqueroH-Index: 8

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Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve a seamless integration between the design and the analysis of thin-walled structures in industrial settings. In this work, we generalize AST-splines to allow multiple extraordinary points within the same face. This generalization drastically increases the flexibility to build geometries using AST-splines; e.g., much coarser meshes can be generated to represent a certain geometry. The AST-spline spaces detailed in this...

#1Guillermo LorenzoH-Index: 8

#2David A. HormuthH-Index: 15

Last. Thomas E. YankeelovH-Index: 52

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Current clinical decision-making in oncology relies on averages of large patient populations to both assess tumor status and treatment outcomes. However, cancers exhibit an inherent evolving heterogeneity that requires an individual approach based on rigorous and precise predictions of cancer growth and treatment response. To this end, we advocate the use of quantitative in vivo imaging data to calibrate mathematical models for the personalized forecasting of tumor development. In this chapter, ...

#1Hugo Casquero (CMU: Carnegie Mellon University)H-Index: 8

#2Carles Bona-CasasH-Index: 17

Last. Yongjie Jessica ZhangH-Index: 12

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We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is particularly challenging due to the higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic knot vectors to obtain discretizations of closed curves with C^2 inter-element continuity. In th...

#1Simone MorgantiH-Index: 18

#2Frederik FahrendorfH-Index: 2

Last. Alessandro RealiH-Index: 45

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#1Radek Bukowski (University of Texas at Austin)H-Index: 32

#2Karl Schulz (University of Texas at Austin)H-Index: 12

Last. Tinsley OdenH-Index: 1

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ABSTRACT Medicine is, in its essence, decision making under uncertainty; The decisions are made about tests to be performed and treatments to be administered. Traditionally the uncertainty in decision making was handled using expertise collected by individual providers, and more recently systematic appraisal of research in the form of evidence-based medicine. The traditional approach has been successfully used in medicine for a very long time. However, it has significant limitations due to the c...

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