Sökning: "multilevel Monte Carlo methods"

Visar resultat 1 - 5 av 12 avhandlingar innehållade orden multilevel Monte Carlo methods.

1. 1. Multiscale Methods and Uncertainty Quantification

   Författare :Daniel Elfverson; Axel Målqvist; Frédéric Legoll; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; multiscale methods; finite element method; discontinuous Galerkin; Petrov-Galerkin; a priori; a posteriori; complex geometry; uncertainty quantification; multilevel Monte Carlo; failure probability; Beräkningsvetenskap med inriktning mot numerisk analys; Scientific Computing with specialization in Numerical Analysis;

   Sammanfattning : In this thesis we consider two great challenges in computer simulations of partial differential equations: multiscale data, varying over multiple scales in space and time, and data uncertainty, due to lack of or inexact measurements.We develop a multiscale method based on a coarse scale correction, using localized fine scale computations. LÄS MER

3. 2. Coarse Graining Monte Carlo Methods for Wireless Channels and Stochastic Differential Equations

   Författare :Håkon Hoel; Anders Szepessy; Ola Hössjer; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Coarse graining; Monte Carlo Methods; Stochastic processes; Numerical analysis; Numerisk analys;

   Sammanfattning : This thesis consists of two papers considering different aspects of stochastic process modelling and the minimisation of computational cost. In the first paper, we analyse statistical signal properties and develop a Gaussian pro- cess model for scenarios with a moving receiver in a scattering environment, as in Clarke’s model, with the generalisation that noise is introduced through scatterers randomly flip- ping on and off as a function of time. LÄS MER

4. 3. Computational Aspects of Lévy-Driven SPDE Approximations

   Författare :Andreas Petersson; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; multilevel Monte Carlo; numerical approximation of stochastic differential equations; multiplicative noise; Lévy processes; finite element method; variance redons; Monte Carlo; weak convergence; Lévy processes;

   Sammanfattning : In order to simulate solutions to stochastic partial differential equations (SPDE) they must be approximated in space and time. In this thesis such fully discrete approximations are considered, with an emphasis on finite element methods combined with rational semigroup approximations. There are several notions of the error resulting from this. LÄS MER

5. 4. Approximating Stochastic Partial Differential Equations with Finite Elements: Computation and Analysis

   Författare :Andreas Petersson; Chalmers tekniska högskola; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Lévy process; Lyapunov equation; white noise; finite element method; multilevel Monte Carlo; Monte Carlo; multiplicative noise; asymptotic mean square stability; stochastic heat equation; covariance operator; weak convergence; generalized Wiener process; numerical approximation; stochastic wave equation; Stochastic partial differential equations;

   Sammanfattning : Stochastic partial differential equations (SPDE) must be approximated in space and time to allow for the simulation of their solutions. In this thesis fully discrete approximations of such equations are considered, with an emphasis on finite element methods combined with rational semigroup approximations. LÄS MER

7. 5. Numerical Methods for Darcy Flow Problems with Rough and Uncertain Data

   Författare :Fredrik Hellman; Axel Målqvist; Auli Niemi; Fritjof Fagerlund; Robert Scheichl; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; numerical homogenization; multiscale methods; rough coefficients; high contrast coefficients; mixed finite elements; cdf estimation; multilevel Monte Carlo methods; Darcy flow problems; Beräkningsvetenskap med inriktning mot numerisk analys; Scientific Computing with specialization in Numerical Analysis;

   Sammanfattning : We address two computational challenges for numerical simulations of Darcy flow problems: rough and uncertain data. The rapidly varying and possibly high contrast permeability coefficient for the pressure equation in Darcy flow problems generally leads to irregular solutions, which in turn make standard solution techniques perform poorly. LÄS MER