1. Introduction

1.1 About the CITCOM dCSE Project

This dCSE project was proposed by Dr Jeroen van Hunen, Department of Earth Sciences, University of Durham along with Dr Charles E. Augarde, School of Engineering, University of Durham. It is targeted at the multigrid (MG) improvements to the CITCOM package, a parallel finite element code designed to solve thermal convection problems relevant to geodynamics. The code is written in C and parallelisation is based on the MPI library.

1.1.1 Project Duration

This project was granted 12 months full time effort for one person to work on a full time basis which, as per a flexible working policy, translates to 15 months time on an 80% basis. It started on January 1, 2009 with a scheduled end date of March 31, 2010 and consisted of three phases, each one dedicated to one or more specific tasks defined in the project proposal and approved as appropriate. A breakdown of these tasks can be described as:

1. Initial project study;
2. Multigrid cycles and smoothers;
3. Mesh refinement.

1.1.2 Project Plan

The aim of this dCSE project is to improve parallel performance and scalability by improving the convergence rate. This would be achieved by implementing/improving algorithmic and programming enhancements for the existing multigrid cycles (where only the V-cycle was initially implemented) with the aim being to implement W-cycle and F-cycle methods, along with mesh refinement and communication amongst the processes. As per proposal, the project is divided into three phases as described in section 1.1.1. After the initial project study in the first phase, during the next two phases the potential candidates for improvements are:

• Phase 2

  (a)

  MG cycles
  By improving the currently implemented V-cycle and implementing W-cycle and F-cycle.

  (b)

  Smoothing
  By replacing the existing Jacobi solver with a Gauss-Seidel solver that will implement a black/red inter-processes communication scheme for the boundary nodes (but see further details on this in Chapter 2).

• Phase 3

  (a)

  Mesh refinement
  By implementing local mesh refinement near the high viscosity gradients.

  (b)

  Improved prolongation and restriction
  Interpolation and transfer of information between MG levels. However, this requires a level of further study/investigation to assess the feasibility and suitability of CITCOM for this implementation.

Further details of these tasks along with implementation and performance improvement results are discussed in the following chapters in detail.

1.2 CITCOM Background

This two dimensional / three dimensional Cartesian version of CITCOM was originally written by Louis Moresi whereas Shijie Zhong later parallelised and improved the code by implementing the full multigrid (MG) algorithm together with a consistent projection scheme, along with the re-ordering of the stiffness matrix and its matrix operations such that only half of the stiffness matrix is stored.