JACC (Journal of the American College of Cardiology), ISSN 0735-1097, 2016, Volume 68, Issue 22, pp. 2488 - 2490

The 2 regression lines differ (p < 0.001), with an upward shift and a decreased slope with dalcetrapib. [...]for any given change in HDL-C, the associated...

Cardiovascular | Internal Medicine | HDL | CARDIAC & CARDIOVASCULAR SYSTEMS | Continuing medical education | C-reactive protein | Coronary heart disease | Cardiac patients | Cholesterol | Proteins | Heart attacks | Cardiovascular disease | Regression analysis | Health risk assessment | Acute coronary syndromes | Low density lipoprotein | Patients

Cardiovascular | Internal Medicine | HDL | CARDIAC & CARDIOVASCULAR SYSTEMS | Continuing medical education | C-reactive protein | Coronary heart disease | Cardiac patients | Cholesterol | Proteins | Heart attacks | Cardiovascular disease | Regression analysis | Health risk assessment | Acute coronary syndromes | Low density lipoprotein | Patients

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 04/2015, Volume 18, Issue 2, pp. 342 - 360

The mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions,...

nonlocal diffusion | boundary value problem | fractional diffusion | well-posed equation | Boundary value problem | Well-posed equation | Fractional diffusion | Nonlocal diffusion | MATHEMATICS, APPLIED | VECTOR CALCULUS | DISPERSION | EQUATIONS | MATHEMATICS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | FINITE-DIFFERENCE APPROXIMATIONS | VOLUME-CONSTRAINED PROBLEMS | Heat equation | Analysis | Differential equations | MATHEMATICS AND COMPUTING

nonlocal diffusion | boundary value problem | fractional diffusion | well-posed equation | Boundary value problem | Well-posed equation | Fractional diffusion | Nonlocal diffusion | MATHEMATICS, APPLIED | VECTOR CALCULUS | DISPERSION | EQUATIONS | MATHEMATICS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | FINITE-DIFFERENCE APPROXIMATIONS | VOLUME-CONSTRAINED PROBLEMS | Heat equation | Analysis | Differential equations | MATHEMATICS AND COMPUTING

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 10/2013, Volume 66, Issue 7, pp. 1245 - 1260

We analyze a nonlocal diffusion operator having as special cases the fractional Laplacian and fractional differential operators that arise in several...

Nonlocal vector calculus | Fractional Laplacian | Finite element methods | Nonlocal diffusion | Fractional Sobolev spaces | Nonlocal operators | MATHEMATICS, APPLIED | TRANSPORT | APPROXIMATION | EQUATIONS | DYNAMICS

Nonlocal vector calculus | Fractional Laplacian | Finite element methods | Nonlocal diffusion | Fractional Sobolev spaces | Nonlocal operators | MATHEMATICS, APPLIED | TRANSPORT | APPROXIMATION | EQUATIONS | DYNAMICS

Journal Article

Applied Mathematics & Optimization, ISSN 0095-4616, 4/2016, Volume 73, Issue 2, pp. 227 - 249

The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as...

Fractional operator | Parameter estimation | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Mathematics | Finite element methods | Nonlocal diffusion | Optimization | Nonlocal operator | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Vector calculus | Numerical and Computational Physics | Control theory | MATHEMATICS, APPLIED | APPROXIMATION | EQUATIONS | Studies | Diffusion | Mathematical analysis | Approximation | Optimal control | Mathematical models | Estimates | Galerkin methods | DIFFUSION EQUATIONS | ERRORS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | APPROXIMATIONS | DIFFUSION | ONE-DIMENSIONAL CALCULATIONS | FINITE ELEMENT METHOD | VARIATIONAL METHODS | KERNELS

Fractional operator | Parameter estimation | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Mathematics | Finite element methods | Nonlocal diffusion | Optimization | Nonlocal operator | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Vector calculus | Numerical and Computational Physics | Control theory | MATHEMATICS, APPLIED | APPROXIMATION | EQUATIONS | Studies | Diffusion | Mathematical analysis | Approximation | Optimal control | Mathematical models | Estimates | Galerkin methods | DIFFUSION EQUATIONS | ERRORS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | APPROXIMATIONS | DIFFUSION | ONE-DIMENSIONAL CALCULATIONS | FINITE ELEMENT METHOD | VARIATIONAL METHODS | KERNELS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2019, Volume 478, Issue 2, pp. 1027 - 1048

We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius....

Nonlocal operator | Finite elements | Regularity of the solution | Fractional Laplacian | Nonlocal diffusion | Variational inequalities | INTERPOLATION | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDED DOMAINS | DIFFUSION-PROBLEMS | Finite. elements

Nonlocal operator | Finite elements | Regularity of the solution | Fractional Laplacian | Nonlocal diffusion | Variational inequalities | INTERPOLATION | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDED DOMAINS | DIFFUSION-PROBLEMS | Finite. elements

Journal Article

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Continuous and discontinuous finite element methods for a peridynamics model of mechanics

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 2011, Volume 200, Issue 9, pp. 1237 - 1250

In contrast to classical partial differential equation models, the recently developed peridynamic nonlocal continuum model for solid mechanics is an...

Finite element methods | Peridynamics | Discontinuous Galerkin methods | ELASTICITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | CONVERGENCE | EQUATION | UNIQUENESS | Finite element method | Models | Analysis | Methods | Differential equations

Finite element methods | Peridynamics | Discontinuous Galerkin methods | ELASTICITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | CONVERGENCE | EQUATION | UNIQUENESS | Finite element method | Models | Analysis | Methods | Differential equations

Journal Article

Computers & Mathematics with Applications, ISSN 0898-1221, 10/2013, Volume 66, Issue 7

We analyze a nonlocal diffusion operator having as special cases the fractional Laplacian and fractional differential operators that arise in several...

Approximation

Approximation

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8.
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Survey of multifidelity methods in uncertainty propagation, inference, and optimization

SIAM Review, ISSN 0036-1445, 2018, Volume 60, Issue 3, pp. 550 - 591

In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These...

Multifidelity | Multifidelity uncertainty propagation | Model reduction | Surrogate models | Multifidelity optimization | Multifidelity statistical inference | Multifidelity uncertainty quantification | multifidelity uncertainty quantification | MATHEMATICS, APPLIED | multifidelity | EFFICIENT GLOBAL OPTIMIZATION | multifidelity uncertainty propagation | surrogate models | model reduction | REDUCED BASIS APPROXIMATION | DESIGN OPTIMIZATION | CHAIN MONTE-CARLO | multifidelity optimization | STOCHASTIC COLLOCATION METHOD | multifidelity statistical inference | PARTIAL-DIFFERENTIAL-EQUATIONS | VARIANCE REDUCTION METHOD | STATISTICAL INVERSE PROBLEMS | MODEL-REDUCTION | PROPER ORTHOGONAL DECOMPOSITION | MATHEMATICS AND COMPUTING

Multifidelity | Multifidelity uncertainty propagation | Model reduction | Surrogate models | Multifidelity optimization | Multifidelity statistical inference | Multifidelity uncertainty quantification | multifidelity uncertainty quantification | MATHEMATICS, APPLIED | multifidelity | EFFICIENT GLOBAL OPTIMIZATION | multifidelity uncertainty propagation | surrogate models | model reduction | REDUCED BASIS APPROXIMATION | DESIGN OPTIMIZATION | CHAIN MONTE-CARLO | multifidelity optimization | STOCHASTIC COLLOCATION METHOD | multifidelity statistical inference | PARTIAL-DIFFERENTIAL-EQUATIONS | VARIANCE REDUCTION METHOD | STATISTICAL INVERSE PROBLEMS | MODEL-REDUCTION | PROPER ORTHOGONAL DECOMPOSITION | MATHEMATICS AND COMPUTING

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2014, Volume 83, Issue 288, pp. 1617 - 1644

Two parallel, non-iterative, multi-physics, domain decomposition methods are proposed to solve a coupled time-dependent Stokes-Darcy system with the...

Finite element method | Error rates | Approximation | Mathematical discontinuity | Partial differential equations | Groundwater flow | Porous materials | Decomposition methods | Boundary conditions | Galerkin methods | Stokes-Darcy model | Domain decomposition methods | Finite element methods | Parallel algorithms | parallel algorithms | MATHEMATICS, APPLIED | COUPLING FLUID-FLOW | domain decomposition methods | GALERKIN METHODS | PARABOLIC PROBLEMS | EXPLICIT-IMPLICIT | CROUZEIX-RAVIART ELEMENT | POROUS-MEDIA FLOW | NUMERICAL-SOLUTION | INTERFACE BOUNDARY-CONDITION | finite element methods | NAVIER-STOKES | FINITE-ELEMENT-METHOD

Finite element method | Error rates | Approximation | Mathematical discontinuity | Partial differential equations | Groundwater flow | Porous materials | Decomposition methods | Boundary conditions | Galerkin methods | Stokes-Darcy model | Domain decomposition methods | Finite element methods | Parallel algorithms | parallel algorithms | MATHEMATICS, APPLIED | COUPLING FLUID-FLOW | domain decomposition methods | GALERKIN METHODS | PARABOLIC PROBLEMS | EXPLICIT-IMPLICIT | CROUZEIX-RAVIART ELEMENT | POROUS-MEDIA FLOW | NUMERICAL-SOLUTION | INTERFACE BOUNDARY-CONDITION | finite element methods | NAVIER-STOKES | FINITE-ELEMENT-METHOD

Journal Article

Water Resources Research, ISSN 0043-1397, 10/2013, Volume 49, Issue 10, pp. 6871 - 6892

Bayesian analysis has become vital to uncertainty quantification in groundwater modeling, but its application has been hindered by the computational cost...

surrogate modeling | uncertainty quantification | high‐order hierarchical basis | groundwater reactive transport | adaptive sparse grid | high-order hierarchical basis | RANDOM INPUT DATA | HETEROGENEOUS MEDIA | WATER RESOURCES | SOLUTE TRANSPORT | FLOW | ENVIRONMENTAL SCIENCES | PARTIAL-DIFFERENTIAL-EQUATIONS | PROBABILISTIC COLLOCATION | INVERSE PROBLEMS | UNCERTAINTY | MONTE-CARLO-SIMULATION | LIMNOLOGY | EFFICIENT | Optimization techniques | Models | Groundwater | Efficiency | Bayesian analysis | Monte Carlo simulation

surrogate modeling | uncertainty quantification | high‐order hierarchical basis | groundwater reactive transport | adaptive sparse grid | high-order hierarchical basis | RANDOM INPUT DATA | HETEROGENEOUS MEDIA | WATER RESOURCES | SOLUTE TRANSPORT | FLOW | ENVIRONMENTAL SCIENCES | PARTIAL-DIFFERENTIAL-EQUATIONS | PROBABILISTIC COLLOCATION | INVERSE PROBLEMS | UNCERTAINTY | MONTE-CARLO-SIMULATION | LIMNOLOGY | EFFICIENT | Optimization techniques | Models | Groundwater | Efficiency | Bayesian analysis | Monte Carlo simulation

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2017, Volume 55, Issue 1, pp. 286 - 304

The definition of partial differential equation models usually involves a set of parameters whose values may vary over a wide range. The solution of even a...

Proper orthogonal decomposition | Reduced-order models | Navier-stokes equations | Ensemble methods | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | RIGHT-HAND SIDES | POD | ensemble methods | ALGORITHM | proper orthogonal decomposition | FLOWS | Navier Stokes equations | reduced-order models | Mathematics

Proper orthogonal decomposition | Reduced-order models | Navier-stokes equations | Ensemble methods | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | RIGHT-HAND SIDES | POD | ensemble methods | ALGORITHM | proper orthogonal decomposition | FLOWS | Navier Stokes equations | reduced-order models | Mathematics

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Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models

CRYOSPHERE, ISSN 1994-0416, 2013, Volume 7, Issue 1, pp. 19 - 29

The manufactured solution technique is used for the verification of computational models in many fields. In this paper, we construct manufactured solutions for...

ISMIP-HOM | GEOGRAPHY, PHYSICAL | GEOSCIENCES, MULTIDISCIPLINARY | HIGHER-ORDER | APPROXIMATION | DYNAMICS | BENCHMARK EXPERIMENTS | FLOW MODELS | Ice sheets | Usage | Models | Construction | Computational fluid dynamics | Computation | Exact solutions | Fluid flow | Mathematical models | Stokes law (fluid mechanics)

ISMIP-HOM | GEOGRAPHY, PHYSICAL | GEOSCIENCES, MULTIDISCIPLINARY | HIGHER-ORDER | APPROXIMATION | DYNAMICS | BENCHMARK EXPERIMENTS | FLOW MODELS | Ice sheets | Usage | Models | Construction | Computational fluid dynamics | Computation | Exact solutions | Fluid flow | Mathematical models | Stokes law (fluid mechanics)

Journal Article

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Concurrent AtC coupling based on a blend of the continuum stress and the atomistic force

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 2007, Volume 196, Issue 45, pp. 4548 - 4560

A concurrent atomistic to continuum (AtC) coupling method is presented in this paper. The problem domain is decomposed into an atomistic sub-domain where fine...

Atomistic to continuum coupling | Concurrent multiscale | Overlap domain decomposition | atomistic to continuum coupling | DEFECTS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | SOLIDS | overlap domain decomposition | concurrent multiscale | MODEL | CRACK | PLASTICITY | Algorithms

Atomistic to continuum coupling | Concurrent multiscale | Overlap domain decomposition | atomistic to continuum coupling | DEFECTS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | SOLIDS | overlap domain decomposition | concurrent multiscale | MODEL | CRACK | PLASTICITY | Algorithms

Journal Article

SIAM Review, ISSN 0036-1445, 12/2012, Volume 54, Issue 4, pp. 667 - 696

A recently developed nonlocal vector calculus is exploited to provide a variational analysis for a general class of nonlocal diffusion problems described by a...

Tensors | Approximation | Flux density | Vector calculus | Wave equations | SURVEY and REVIEW | Boundary conditions | Laplacians | Mathematical functions | Sobolev spaces | Modeling | Fractional operator | Nonlocal operator | Superdiffusion | Nonlocal heat conduction | Anomalous diffusion | Monlocal diffusion | Peridynamics | Finite element methods | Fractional Laplacian | Fractional Sobolev spaces | fractional Sobolev spaces | MATHEMATICS, APPLIED | nonlocal diffusion | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | LONG-RANGE FORCES | nonlocal heat conduction | SYMMETRIC JUMP-PROCESSES | SOBOLEV SPACES | TRANSPORT | fractional operator | nonlocal operator | finite element methods | fractional Laplacian | vector calculus | superdiffusion | DYNAMICS | FRACTIONAL ADVECTION-DISPERSION | anomalous diffusion | OPERATORS | peridynamics | Finite element method | Usage | Diffusion processes | Analysis | Calculus | Research | Methods | Studies | Mathematical models | Laplace transforms | Diffusion | Heat conductivity

Tensors | Approximation | Flux density | Vector calculus | Wave equations | SURVEY and REVIEW | Boundary conditions | Laplacians | Mathematical functions | Sobolev spaces | Modeling | Fractional operator | Nonlocal operator | Superdiffusion | Nonlocal heat conduction | Anomalous diffusion | Monlocal diffusion | Peridynamics | Finite element methods | Fractional Laplacian | Fractional Sobolev spaces | fractional Sobolev spaces | MATHEMATICS, APPLIED | nonlocal diffusion | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | LONG-RANGE FORCES | nonlocal heat conduction | SYMMETRIC JUMP-PROCESSES | SOBOLEV SPACES | TRANSPORT | fractional operator | nonlocal operator | finite element methods | fractional Laplacian | vector calculus | superdiffusion | DYNAMICS | FRACTIONAL ADVECTION-DISPERSION | anomalous diffusion | OPERATORS | peridynamics | Finite element method | Usage | Diffusion processes | Analysis | Calculus | Research | Methods | Studies | Mathematical models | Laplace transforms | Diffusion | Heat conductivity

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 06/2017, Volume 319, Issue C, pp. 217 - 239

Simulation-based optimization of acoustic liner design in a turbofan engine nacelle for noise reduction purposes can dramatically reduce the cost and time...

Proper orthogonal decomposition | Stochastic Helmholtz equation | Conditional value at risk | Turbofan noise reduction | RADIATED ENGINE NOISE | PRECONDITIONERS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | HELMHOLTZ-EQUATION | ENGINEERING, MULTIDISCIPLINARY | ACOUSTIC LINER | Models | Algorithms | Noise control | Mathematical optimization | Analysis | Mathematics - Optimization and Control

Proper orthogonal decomposition | Stochastic Helmholtz equation | Conditional value at risk | Turbofan noise reduction | RADIATED ENGINE NOISE | PRECONDITIONERS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | HELMHOLTZ-EQUATION | ENGINEERING, MULTIDISCIPLINARY | ACOUSTIC LINER | Models | Algorithms | Noise control | Mathematical optimization | Analysis | Mathematics - Optimization and Control

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2014, Volume 52, Issue 1, pp. 243 - 273

A control problem constrained by a nonlocal steady diffusion equation that arises in several applications is studied. The control is the right-hand side...

Nonlocal operator | Nonlocal vector calculus | Superdiffusion | Control theory | Finite element methods | Nonlocal diffusion | Fractional Sobolev spaces | Optimization | fractional Sobolev spaces | MATHEMATICS, APPLIED | nonlocal vector calculus | control theory | APPROXIMATION | optimization | nonlocal operator | finite element methods | nonlocal diffusion | superdiffusion | AUTOMATION & CONTROL SYSTEMS

Nonlocal operator | Nonlocal vector calculus | Superdiffusion | Control theory | Finite element methods | Nonlocal diffusion | Fractional Sobolev spaces | Optimization | fractional Sobolev spaces | MATHEMATICS, APPLIED | nonlocal vector calculus | control theory | APPROXIMATION | optimization | nonlocal operator | finite element methods | nonlocal diffusion | superdiffusion | AUTOMATION & CONTROL SYSTEMS

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 11/2013, Volume 266, pp. 185 - 204

We investigate interface problems in nonlocal diffusion and demonstrate how to reformulate and generalize the classical treatment of interface problems in the...

Nonlocal diffusion | Interface conditions | Multiscale modeling | Interface problems | VECTOR CALCULUS | APPROXIMATION | EQUATIONS | DAMAGE | SCHEME | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | INTEGRODIFFERENTIAL MODEL | PERIDYNAMICS | Computer simulation | Mathematical analysis | Conservation | Derivation | Horizon | Mathematical models | Diffusion

Nonlocal diffusion | Interface conditions | Multiscale modeling | Interface problems | VECTOR CALCULUS | APPROXIMATION | EQUATIONS | DAMAGE | SCHEME | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | INTEGRODIFFERENTIAL MODEL | PERIDYNAMICS | Computer simulation | Mathematical analysis | Conservation | Derivation | Horizon | Mathematical models | Diffusion

Journal Article

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, ISSN 0363-0129, 2019, Volume 57, Issue 1, pp. 241 - 263

The optimality system is derived for an optimal control problem governed by a time-fractional PDE. A fully discrete finite element method along with...

MATHEMATICS, APPLIED | time-fractional equation | finite element method | optimal control | DIFFUSION | convolution quadrature | error estimates | EQUATION | AUTOMATION & CONTROL SYSTEMS

MATHEMATICS, APPLIED | time-fractional equation | finite element method | optimal control | DIFFUSION | convolution quadrature | error estimates | EQUATION | AUTOMATION & CONTROL SYSTEMS

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 07/2019, Volume 351, Issue C, pp. 379 - 403

Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial...

Navier–Stokes equations | k-means clustering | Proper orthogonal decomposition | Reduced-order modeling | Steady bifurcations | Localized reduced bases | FLOW | REGIMES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | REDUCTION | CHANNEL | DYNAMICS | Navier-Stokes equations | Usage | Models | Algorithms | Differential equations | Parameters | Partial differential equations | Clusters | Bifurcations | Mathematical models | Reduced order models | Proper Orthogonal Decomposition | Optimization

Navier–Stokes equations | k-means clustering | Proper orthogonal decomposition | Reduced-order modeling | Steady bifurcations | Localized reduced bases | FLOW | REGIMES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | REDUCTION | CHANNEL | DYNAMICS | Navier-Stokes equations | Usage | Models | Algorithms | Differential equations | Parameters | Partial differential equations | Clusters | Bifurcations | Mathematical models | Reduced order models | Proper Orthogonal Decomposition | Optimization

Journal Article