Related papers: Stochastic domain decomposition for time dependent…
The efficient generation of meshes is an important step in the numerical solution of various problems in physics and engineering. We are interested in situations where global mesh quality and tight coupling to the physical solution is…
We use a time-relaxed linear grid generator of Winslow type to propose a new deterministic-stochastic domain decomposition approach to the generation of adaptive moving meshes. The method uses the probabilistic form of the exact solution of…
A fast method is presented for adaptive moving mesh generation in multi-dimensions using a domain decomposition parabolic Monge-Amp\`ere approach. The domain decomposition procedure employed here is non-iterative and involves splitting the…
We present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each…
Domain discretization is considered a dominant part of solution procedures for solving partial differential equations. It is widely accepted that mesh generation is among the most cumbersome parts of the FEM analysis and often requires…
Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…
The moving mesh PDE (MMPDE) method for variational mesh generation and adaptation is studied theoretically at the discrete level, in particular the nonsingularity of the obtained meshes. Meshing functionals are discretized geometrically and…
In this work, we propose a new stochastic domain decomposition method for solving steady-state partial differential equations (PDEs) with random inputs. Based on the efficiency of the Variable-separation (VS) method in simulating stochastic…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…
We extend stochastic basis adaptation and spatial domain decomposition methods to solve time varying stochastic partial differential equations (SPDEs) with a large number of input random parameters. Stochastic basis adaptation allows the…
This work describes a domain embedding technique between two non-matching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is…
In this paper, we present a feature-aware SPH method for the concurrent and automated isotropic unstructured mesh generation. Two additional objectives are achieved with the proposed method compared to the original SPH-based mesh generator…
We demonstrate an approach to the numerical solution of nonlinear stochastic differential equations with Markovian switching. Such equations describe the stochastic dynamics of processes where the drift and diffusion coefficients are…
Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discretization. By leveraging Gaussian process regression and…
Mesh generation remains a key technology in many areas where numerical simulations are required. As numerical algorithms become more efficient and computers become more powerful, the percentage of time devoted to mesh generation becomes…
Geophysical model domains typically contain irregular, complex fractal-like boundaries and physical processes that act over a wide range of scales. Constructing geographically constrained boundary-conforming spatial discretizations of these…
In this paper, we propose a consistent parallel unstructured mesh generator based on a multi-phase SPH method. A set of physics-motivated modeling equations are developed to achieve the targets of domain decomposition, communication volume…
Stochastic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell's equations as used in the magnetotelluric method. The stochastic form of the exact solution of Maxwell's equations is evaluated using…
We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field during materials processing. Our numerical approach uses the systematic renormalization-group formulation of the phase field…