MultilevelEstimators

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MultilevelEstimators is a Julia package for Multilevel Monte Carlo simulations. It contains the following methods:

• Monte Carlo (MC) and Quasi-Monte Carlo (QMC)

• Multilevel Monte Carlo (MLMC) and Multilevel Quasi-Monte Carlo (MLQMC)

• Multi-Index Monte Carlo (MIMC) and Multi-Index Quasi-Monte Carlo (MIQMC)

• Adaptive Multi-Index Monte Carlo (A-MIMC) and Adaptive Multi-Index Quasi-Monte Carlo (A-MIQMC)

• NEW! Unbiased Multilevel Monte Carlo (U-MLMC) and Unbiased Multilevel Quasi-Monte Carlo (U-MLQMC)

• NEW! Unbiased Multi-Index Monte Carlo (U-MIMC) and Unbiased Multi-Index Quasi-Monte Carlo (U-MIQMC)

Installation

The package is not (yet) registered in METADATA.jl but can be installed with

pkg> add https://github.com/PieterjanRobbe/MultilevelEstimators.jl

Read the instructions in the documentation for more details on how to install MultilevelEstimators and its dependencies.

Example

An example for a PDE with random coefficients can be found in the example section in the documentation.

Documentation

Documentation is available here.

Related Packages

• Reporter.jl — automatic generation of diagnostic information and reports for a MultilevelEstimators simulation
• LognormalDiffusionProblems.jl — a package with a complete MultilevelEstimators setup for a 2d elliptic PDE with random coefficients