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Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochas ...
We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any ord ...
This article is devoted to the analysis of a Monte Carlo method to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. We consider the case of independent and identically distributed coefficients, and adopt the p ...
The first two authors and Kohnen have recently introduced a new class of modular objects called locally harmonic Maass forms, which are annihilated almost everywhere by the hyperbolic Laplacian operator. In this paper, we realize these locally harmonic Maa ...
In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of p ...
In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remap ...
The fractional Laplacian (-Delta)(gamma/2) commutes with the primary coordination transformations in the Euclidean space Rd: dilation, translation and rotation, and has tight link to splines, fractals and stable Levy processes. For 0 < gamma < d, its inver ...
We propose a Reduced Basis method for the solution of parametrized optimal control problems with control constraints for which we extend the method proposed in Dedè, L. (SIAM J. Sci. Comput. 32:997, 2010) for the unconstrained problem. The case of a linear ...
We investigate multilevel Schwarz domain decomposition preconditioners, to efficiently solve linear systems arising from numerical discretizations of elliptic partial differential equations by the finite element method. In our analysis we deal with unstruc ...
A high-order discretization consisting of a tensor product of the Fourier collocation and discontinuous Galerkin methods is presented for numerical modeling of magma dynamics. The physical model is an advection-reaction type system consisting of two hyperb ...
