Parallel solution of initial value problems using the parareal method

Abstract

This thesis examines the parareal method, which is on of the first parallel-in-time integration methods. First, we present an overwiev of sequential methods for solving initial value problems, focusing on Forward Eulers's method and 4th order Runge-Kutta method. Then we describe parareal method, its algorithm and its convergence theorems. Then we discuss harware and software used for parallel computations and show different approaches to parallel programming with special emphasis on shared-memory multithreading using OpenMP API. Finally implementation of parareal algorithm in C++ language using OpenMP is outlined and numerical experiments are conducted on 1-dimensional and 2-dimensional heat equation problems.