List of Figures

• 2.1. A standard rectangular element in 2D
• 2.2. A standard brick element in 3D
• 2.3. A CITCOM rectangular element in 2D
• 2.4. A CITCOM brick element in 3D
• 2.5. A CITCOM rectangular element and local nodes relationship
• 2.6. A CITCOM brick element and local nodes relationship
• 2.7. A sample CITCOM mesh of 8 (4x2) rectangular elements
• 2.8. A sample CITCOM mesh of 16 (4x2x2) brick elements
• 3.1. Multigrid V-cycle Scheme
• 3.2. Multigrid W-cycle Scheme
• 3.3. FMG(V)-cycle Scheme
• 3.4. Parallel performance and scaling of MG schemes for a simple 2D test problem
• 3.5. Temperature and velocity field charts for a simple 2D test problem
• 3.6. Parallel performance and scaling of MG schemes for a simple 3D test problem
• 3.7. Temperature and velocity field charts for a simple 3D test problem
• 3.8. Parallel performance and scaling of MG schemes for a complex 2D test problem
• 3.9. Temperature and velocity field charts for a complex 2D test problem
• 3.10. Parallel performance and scaling of MG schemes for a complex 3D test problem
• 3.11. Temperature and velocity field charts for a complex 3D test problem
• 3.12. Examples of uniform (left) and non-uniform (right) refinement
• 4.1. A two element mesh in 2D at level 0
• 4.2. A local refinement without obeying one level difference rule
• 4.3. A local mesh refinement forbidden by one level difference rule
• 4.4. A local refinement by one level difference rule
• 4.5. A coarse mesh of 48 elements in two dimension
• 4.6. A coarse mesh of 24 elements in three dimension
• 4.7. Local refinement of the coarse mesh at top of the domain in two dimension
• 4.8. Local refinement of the coarse mesh at top of the domain in three dimension (for a relatively smaller mesh)