3. Theory

• 3.1. Domain Definition
• 3.2. Governing Equations
  • 3.2.1. Generalized Conservation Equation
  • 3.2.2. Statement of the Transient Problem
  • 3.2.3. Statement of the Stationary Problem
  • 3.2.4. Equations Aria Solves
  • 3.2.5. Notes on Solid Mechanics
• 3.3. Boundary Conditions
  • 3.3.1. Dirichlet (Specified Value)
  • 3.3.2. Neumann (Specified Flux)
  • 3.3.3. Fluxbp
  • 3.3.4. Disting
  • 3.3.5. Rotated
  • 3.3.6. Interface
  • 3.3.7. Colloc Prefix
  • 3.3.8. Lumped Prefix
• 3.4. Sources
• 3.5. Interface Conditions
  • 3.5.1. Perfect or Tied Contact
  • 3.5.2. Contact Resistance
• 3.6. Radiation
  • 3.6.1. Surface Radiation
  • 3.6.2. Enclosure Radiation
  • 3.6.3. Banded Wavelength Enclosure Radiation
• 3.7. Contact
  • 3.7.1. Contact Interface
  • 3.7.2. Contact Enforcement
• 3.8. Discretization
  • 3.8.1. Weak Statement of the Stationary Problem
  • 3.8.2. Well-posed Problems
  • 3.8.3. Galerkin Approximation for the Stationary Problem
  • 3.8.4. Weak Statement of the Transient Problem
  • 3.8.5. Galerkin Approximation for the Transient Problem
  • 3.8.6. Mass Lumping
  • 3.8.7. Time Discretization
• 3.9. Finite Element Approximation
  • 3.9.1. Element Integration
  • 3.9.2. Linear Master Elements
• 3.10. CVFEM
  • 3.10.1. Integral Form
  • 3.10.2. CVFEM Operators
• 3.11. Solution Strategy
  • 3.11.1. Time Integration
  • 3.11.2. Predictor-Corrector
• 3.12. Coupling
  • 3.12.1. One Way Coupling
  • 3.12.2. Two Way Coupling
• 3.13. Arbitrary Lagrangian-Eulerian
• 3.14. Teko Heuristic Multiphysics Preconditioner
  • 3.14.1. Convergence of Block Gauss-Seidel
  • 3.14.2. Linear Ordering Problem for Block Gauss-Seidel
  • 3.14.3. Block Merging Problem for Block Gauss-Seidel
  • 3.14.4. Choosing Sub-block Solvers for Block Gauss-Seidel