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A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
16 references·16 citing·20 second hopsampled
A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties (2009)A domain adaptive stochastic collocation …An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)An adaptive hierarchical spar…Sparse grid collocation schemes for stochastic natural convection problems (2007)Sparse grid collocation schem…Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)Multi-Element Generalized Pol…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)An adaptive multi-element gen…Uncertainty propagation using Wiener–Haar expansions (2004)Uncertainty propagation using…Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes (2004)Numerical Challenges in the U…Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Galerkin Finite Element Appro…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos (2002)Modeling uncertainty in stead…A Stochastic Projection Method for Fluid Flow (2002)A Stochastic Projection Metho…Solution of stochastic partial differential equations using Galerkin finite element techniques (2001)Solution of stochastic partia…A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (2000)A Comparison of Three Methods…A state-of-the-art report on computational stochastic mechanics (1997)A state-of-the-art report on …Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (1979)A Comparison of Three Methods…An uncertainty quantification framework for multiscale parametrically homogenized constitutive models (PHCMs) of polycrystalline Ti alloys (2021)An uncertainty quantification…The effects of clinically‐derived parametric data uncertainty in patient‐specific coronary simulations with deformable walls (2020)The effects of clinically‐der…Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis (2018)Stochastic collocation approa…Multi-fidelity stochastic collocation method for computation of statistical moments (2017)Multi-fidelity stochastic col…Stochastic Collocation Methods for Nonlinear Parabolic Equations with Random Coefficients (2016)Stochastic Collocation Method…A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling (2016)A generalized multi-resolutio…Uncertainty Quantification for Electromagnetic Systems Using ASGC and DGTD Method (2015)Uncertainty Quantification fo…Local Polynomial Chaos Expansion for Linear Differential Equations with High Dimensional Random Inputs (2015)Local Polynomial Chaos Expans…Computational Aspects of Stochastic Collocation with Multifidelity Models (2014)Computational Aspects of Stoc…Simplex stochastic collocation with ENO-type stencil selection for robust uncertainty quantification (2013)Simplex stochastic collocatio…Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions (2013)Minimal multi-element stochas…Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation (2012)Stochastic Collocation Method…Simplex Stochastic Collocation with Random Sampling and Extrapolation for Nonhypercube Probability Spaces (2012)Simplex Stochastic Collocatio…Refinement Criteria for Simplex Stochastic Collocation with Local Extremum Diminishing Robustness (2012)Refinement Criteria for Simpl…A semi-intrusive deterministic approach to uncertainty quantification in non-linear fluid flow problems (2012)A semi-intrusive deterministi…A data‐driven stochastic collocation approach for uncertainty quantification in MEMS (2010)A data‐driven stochastic coll…Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012)Random vibration and statistical linearization (1990)Verification and Validation in Computational Science and Engineering (1998)Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2004)Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)An Introduction to Computational Stochastic PDEs (2014)Large Sample Properties of Simulations Using Latin Hypercube Sampling (1987)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)A review of techniques for parameter sensitivity analysis of environmental models (1994)Importance measures in global sensitivity analysis of nonlinear models (1996)Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems (2003)Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles (2011)
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References

  • 2000A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code8,233 cited
  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 1979A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code3,766 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
  • 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
  • 2002Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos552 cited
  • 2002A Stochastic Projection Method for Fluid Flow503 cited
  • 2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures498 cited
  • 2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes451 cited
  • 2009An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations447 cited
  • 2004Uncertainty propagation using Wiener–Haar expansions438 cited
  • 1997A state-of-the-art report on computational stochastic mechanics

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424 cited
  • 2001Solution of stochastic partial differential equations using Galerkin finite element techniques414 cited
  • 2007Sparse grid collocation schemes for stochastic natural convection problems401 cited
  • Cited by

    • 2012Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation73 cited
    • 2014Computational Aspects of Stochastic Collocation with Multifidelity Models67 cited
    • 2012Simplex Stochastic Collocation with Random Sampling and Extrapolation for Nonhypercube Probability Spaces63 cited
    • 2013Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions50 cited
    • 2012A semi-intrusive deterministic approach to uncertainty quantification in non-linear fluid flow problems44 cited
    • 2020The effects of clinically‐derived parametric data uncertainty in patient‐specific coronary simulations with deformable walls44 cited
    • 2013Simplex stochastic collocation with ENO-type stencil selection for robust uncertainty quantification40 cited
    • 2015Local Polynomial Chaos Expansion for Linear Differential Equations with High Dimensional Random Inputs39 cited
    • 2017Multi-fidelity stochastic collocation method for computation of statistical moments39 cited
    • 2021An uncertainty quantification framework for multiscale parametrically homogenized constitutive models (PHCMs) of polycrystalline Ti alloys31 cited
    • 2016A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling30 cited
    • 2016Stochastic Collocation Methods for Nonlinear Parabolic Equations with Random Coefficients30 cited
    • 2018Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis27 cited
    • 2012Refinement Criteria for Simplex Stochastic Collocation with Local Extremum Diminishing Robustness26 cited
    • 2015Uncertainty Quantification for Electromagnetic Systems Using ASGC and DGTD Method26 cited
    • 2010A data‐driven stochastic collocation approach for uncertainty quantification in MEMS26 cited