相关论文: Domain Decomposition of Stochastic PDEs: Developme…
Two-level domain decomposition (DD) methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level…
The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…
Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…
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…
In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by Xu…
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…
Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parameters, constitutive relations, initial/boundary conditions,…
Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
Elliptic partial differential equations (PDEs) frequently arise in continuum descriptions of physical processes relevant to science and engineering. Multilevel preconditioners represent a family of scalable techniques for solving discrete…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the…
Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
Common techniques for the spatial discretisation of PDEs on a macroscale grid include finite difference, finite elements and finite volume methods. Such methods typically impose assumed microscale structures on the subgrid fields, so…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
An acoustic wave propagation problem with a log normal random field approximation for wave speed is solved using a sampling-free intrusive stochastic Galerkin approach. The stochastic partial differential equation with the inputs and…
In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…