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- Dongbin Xiu, George E. Karniadakis
- SIAM J. Scientific Computing
- 2002

We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wienerâ€™s polynomial chaos. Specifically, we represent the stochastic processesâ€¦ (More)

We formulate a Multi-Element generalized Polynomial Chaos (ME-gPC) method to deal with long-term integration and discontinuities in stochastic differential equations. We first present this method forâ€¦ (More)

We present a new algorithm to model the input uncertainty and its propagation in incompressible flow simulations. The stochastic input is represented spectrally by employing orthogonal polynomialâ€¦ (More)

- Dmitry A. Fedosov, Bruce Caswell, George E. Karniadakis
- Biophysical journal
- 2010

Red blood cells (RBCs) have highly deformable viscoelastic membranes exhibiting complex rheological response and rich hydrodynamic behavior governed by special elastic and bending properties and byâ€¦ (More)

- Xiaoliang Wan, George E. Karniadakis
- SIAM J. Scientific Computing
- 2006

We develop a multi-element generalized polynomial chaos (ME-gPC) method for arbitrary probability measures and apply it to solve ordinary and partial differential equations with stochastic inputs.â€¦ (More)

- Igor V. Pivkin, George E. Karniadakis
- Physical review letters
- 2008

We develop a systematic coarse-graining procedure for modeling red blood cells (RBCs) using arguments based on mean-field theory. The three-dimensional RBC membrane model takes into account theâ€¦ (More)

- Jasmine Foo, George E. Karniadakis
- J. Comput. Physics
- 2010

We combine multi-element polynomial chaos with analysis of variance (ANOVA) functional decomposition to enhance the convergence rate of polynomial chaos in high dimensions and in problems with lowâ€¦ (More)

We present a generalized polynomial chaos algorithm for the solution of stochastic elliptic partial differential equations subject to uncertain inputs. In particular, we focus on the solution of theâ€¦ (More)

- Jasmine Foo, Xiaoliang Wan, George E. Karniadakis
- J. Comput. Physics
- 2008

Stochastic spectral methods are numerical techniques for approximating solutions to partial differential equations with random parameters. In this work, we present and examine the multi-elementâ€¦ (More)

- G-S. Karamanos, George E. Karniadakis
- 2000

A new simulation approach for high Reynolds number turbulent flows is developed, combining concepts of monotonicity in nonlinear conservation laws with concepts of large-eddy simulation. The spectralâ€¦ (More)