Finite elements for Matérn-type random fields: uncertainty in computational mechanics and design optimization

Finite element methods applied to problems in solid mechanics (74S05) Optimization of other properties in solid mechanics (74P10) Stochastic and other probabilistic methods applied to problems in solid mechanics (74S60)

Cites Work

An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach
The Rational SPDE Approach for Gaussian Random Fields With General Smoothness
On projection methods, convergence and robust formulations in topology optimization
A new level-set based approach to shape and topology optimization under geometric uncertainty
Topology optimization considering material and geometric uncertainties using stochastic collocation methods
Parallel framework for topology optimization using the method of moving asymptotes
Robust topology optimization accounting for spatially varying manufacturing errors
Robust topology optimization under loading uncertainty based on linear elastic theory and orthogonal diagonalization of symmetric matrices
Numerically solving an equation for fractional powers of elliptic operators
Fractional powers of closed operators and the semigroups generated by them
Isotropic Gaussian random fields on the sphere: regularity, fast simulation and stochastic partial differential equations
\textit{BoomerAMG}: A parallel algebraic multigrid solver and preconditioner
An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loève and polynomial expansions.
Material interpolation schemes in topology optimization
Fast random field generation with $H$-matrices
Generalized harmonic analysis.
Korrelationstheorie der stationären stochastischen Prozesse
Advances in Gaussian random field generation: a review
A primal-dual algorithm for risk minimization
MFEM: a modular finite element methods library
What is the fractional Laplacian? A comparative review with new results
Maximum length scale in density based topology optimization
Risk-averse structural topology optimization under random fields using stochastic expansion methods
On sinc quadrature approximations of fractional powers of regularly accretive operators
Tensor FEM for spectral fractional diffusion
A numerical study of the homogeneous elliptic equation with fractional boundary conditions
Robust shape optimization of continuous structures via the level set method
Karhunen-Loève approximation of random fields by generalized fast multipole methods
Exponential convergence of \textit{hp} FEM for spectral fractional diffusion in polygons
Statistically equivalent surrogate material models: impact of random imperfections on the elasto-plastic response
Risk-averse design of tall buildings for uncertain wind conditions
Filters in topology optimization
Geometrical Structure of Laplacian Eigenfunctions
Filters in topology optimization based on Helmholtz-type differential equations
Topology optimization with geometric uncertainties by perturbation techniques
Spatial Matérn Fields Driven by Non-Gaussian Noise
Geostatistical Modelling Using Non-Gaussian Matérn Fields
Fast simulation of Gaussian random fields
A fractional PDE model for turbulent velocity fields near solid walls
Hemodynamics of Cerebral Aneurysms
An Effective Fluid-Structure Interaction Formulation for Vascular Dynamics by Generalized Robin Conditions
Spectral Methods for Uncertainty Quantification
The method of moving asymptotes—a new method for structural optimization
The spatial structure of neutral atmospheric surface-layer turbulence
Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix
Adaptive Sampling Strategies for Stochastic Optimization
Analysis of Circulant Embedding Methods for Sampling Stationary Random Fields
$hp$-Finite Elements for Fractional Diffusion
Optimal Control of PDEs under Uncertainty
Algebraic multigrid methods
Efficient White Noise Sampling and Coupling for Multilevel Monte Carlo with Nonnested Meshes
Positive Approximations of the Inverse of Fractional Powers of SPD M-Matrices
A BLOCK CIRCULANT EMBEDDING METHOD FOR SIMULATION OF STATIONARY GAUSSIAN RANDOM FIELDS ON BLOCK-REGULAR GRIDS
Surface Finite Element Approximation of Spherical Whittle--Matérn Gaussian Random Fields
A Statistical Framework for Generating Microstructures of Two-Phase Random Materials: Application to Fatigue Analysis
Analysis of Boundary Effects on PDE-Based Sampling of Whittle--Matérn Random Fields
Preconditioning
Numerical approximation of fractional powers of elliptic operators
Achieving minimum length scale in topology optimization using nodal design variables and projection functions
Restricted delaunay triangulations and normal cycle
An Extension Problem Related to the Fractional Laplacian
Risk-Averse PDE-Constrained Optimization Using the Conditional Value-At-Risk
The AAA Algorithm for Rational Approximation
ON STATIONARY PROCESSES IN THE PLANE
Efficient generation of conditional simulations by Chebyshev matrix polynomial approximations to the symmetric square root of the covariance matrix
Moving averages for Gaussian simulation in two and three dimensions
General joint conditional simulations using a fast Fourier transform method
Random heterogeneous materials. Microstructure and macroscopic properties
An adaptive sampling augmented Lagrangian method for stochastic optimization with deterministic constraints
Numerical methods for fractional diffusion
Solving time-fractional differential equations via rational approximation
Stochastic PDE representation of random fields for large-scale Gaussian process regression and statistical finite element analysis
Adaptive sampling strategies for risk-averse stochastic optimization with constraints
Scalable parallel scheme for sampling of Gaussian random fields over very large domains
Numerical approximation of Gaussian random fields on closed surfaces
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