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Journal of Computational Physics, ISSN 0021-9991, 09/2013, Volume 248, pp. 87 - 108
We consider elliptic stochastic partial differential equations (SPDEs) with random coefficients and solve them by expanding the solution using generalized... 
Generalized polynomial chaos | Compressive sensing | High-dimensions | Chebyshev probability measure
Journal Article
2017, Applied Mathematical Sciences, ISBN 3319575112, Volume 196
This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book... 
Numerical analysis | Partial differential equations | Mathematics | Probabilities
Web Resource
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2006, Volume 28, Issue 3, pp. 901 - 928
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 10/2019, p. 109020
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 03/2018, Volume 357, p. 125
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 02/2019, Volume 378, pp. 44 - 62
Journal Article
JOURNAL OF COMPUTATIONAL PHYSICS, ISSN 0021-9991, 09/2013, Volume 248, pp. 87 - 108
Journal Article
COMPUTATIONAL MECHANICS, ISSN 0178-7675, 08/2019, Volume 64, Issue 2, pp. 409 - 416
This work introduces the concept of parametric Gaussian processes (PGP), which is built upon the seemingly self-contradictory idea of making Gaussian processes... 
Gaussian process regression | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Big data | Probabilistic machine learning | Gaussian processes
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 05/2017, Volume 336, p. 143
We consider the viscous Burgers equation with a fractional nonlinear term as a model involving non-local nonlinearities in conservation laws, which,... 
Studies | Viscosity | Conservation laws | Spectral element method | Computational mathematics | Mathematical models | Spectra | Galerkin method | Burgers equation | Nonlinear systems | Spectral methods
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 05/2017, Volume 336, p. 481
We have developed a new single-particle dissipative particle dynamics (DPD) model for anisotropic particles with different shapes, e.g., prolate or oblate... 
Computational fluid dynamics | Colloids | Oblate spheroids | Fluid flow | Variations | Hydrodynamics | Mapping | Aspect ratio | Model accuracy | Spheroids | Ellipsoids | Studies | Drag | Anisotropy | Energy dissipation | Dissipation | Angular momentum | Models | Diffusion
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 12/2018, Volume 374, p. 121
We consider a new prototype problem in domain decomposition with the solution in one domain governed by a known partial differential equation (PDE) whereas the... 
Helmholtz equations | Gaussian process | Partial differential equations | Normal distribution | Decomposition | Sensors | Artificial intelligence | Domain decomposition
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 11/2017, Volume 348, p. 683
This work leverages recent advances in probabilistic machine learning to discover governing equations expressed by parametric linear operators. Such equations... 
Uncertainty | Inverse problems | Gaussian process | Computer simulation | Normal distribution | Mathematical analysis | Differential equations | Machine learning | Gaussian distribution | Linear equations | Artificial intelligence | Linear operators
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 09/2017, Volume 324, p. 512
We develop a new C0-continuous Petrov-Galerkin spectral element method for one-dimensional fractional elliptic problems of the form ..., subject to homogeneous... 
Linear systems | Construction standards | Stiffness matrix | Boundary conditions | Spectra | Matrix methods | Studies | Accuracy | Efficiency | Spectral element method | Models | Galerkin method | Conditioning
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 04/2017, Volume 335, p. 736
For more than two centuries, solutions of differential equations have been obtained either analytically or numerically based on typically well-behaved forcing... 
Studies | Uncertainty | Integration | Gaussian process | Differential equations | Machine learning | Linear equations | Well posed problems | Artificial intelligence
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 02/2018, Volume 355, p. 534
Dissipative particle dynamics (DPD) is an effective Lagrangian method for modeling complex fluids in the mesoscale regime but so far it has been limited to... 
Deformation | Computational fluid dynamics | Computer simulation | Slip | Variations | Boundary conditions | Formability | Navier Stokes equations | Surfactants | Object recognition | Drawings | Penetration | Laminar flow | Dissipation | Couette flow | Computational physics | Cylinders | Navier-Stokes equations
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 05/2017, Volume 318, p. 193
In this work, a finite difference method of tunable accuracy for fractional differential equations (FDEs) with end-point singularities is developed. Modified... 
Studies | Operators (mathematics) | Accuracy | Fourier transforms | Boundary value problems | Singularities | Differential equations | Finite difference method
Journal Article
The Journal of Chemical Physics, ISSN 0021-9606, 09/2019, Volume 151, Issue 10, p. 104101
We study the intrinsic nature of the finite system-size effect in estimating shear viscosity of dilute and dense fluids within the framework of the Green–Kubo... 
HARD-SPHERE FLUID | AUTOCORRELATION-FUNCTION | TRANSPORT | TIME-CORRELATION FUNCTIONS | LIQUID | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | COEFFICIENTS | CHEMISTRY, PHYSICAL | SIMULATION | POINT | Viscosity | Molecular dynamics | Size effects | Autocorrelation functions | Shear viscosity | Density
Journal Article
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