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A Series of Example Programs

The following series of example programs have been designed to get you started on the right foot. They are arranged into categories based on which library features they demonstrate.

• Introduction
  1. Creation of a Mesh Object
  2. Defining a Simple System
  3. Solving a 2D Poisson Problem
  4. Solving a 2D or 3D Poisson Problem in Parallel
  5. Run-time Quadrature Rule Selection
• Systems of Equations
  1. Stokes Equations
  2. Unsteady Nonlinear Navier-Stokes
  3. Navier-Stokes with SCALAR Lagrange Multiplier
  4. Linear Elastic Cantilever
  5. Linear Elastic Cantilever with Constraint
  6. 3D Linear Elastic Cantilever
  7. Large Deformation Elasticity
  8. Small-sliding Contact
  9. Linear elasticity with periodic constraints
• Transient Systems
  1. Solving a Transient Linear System in Parallel
  2. The Newmark System and the Wave Equation
  3. Explicit FV/DG Formulation of the 2D Advection Equation
• Adaptivity
  1. Solving 1D PDE Using Adaptive Mesh Refinement
  2. Solving a Transient System with Adaptive Mesh Refinement
  3. Laplace's Equation in an L-Shaped Domain
  4. Solving the Biharmonic Equation
  5. Periodic Boundary Conditions
• Eigenproblems
  1. Solving an Eigen Problem
  2. Solving a generalized Eigen Problem
  3. Can you "hear the shape" of a drum?
  4. Solving a Condensed EigenSystem
• Subdomains
  1. Solving on a Subdomain
  2. Subdomain-Restricted Variables
  3. Integrating Discontinuous Data
• FEMSystem Framework
  1. Unsteady Navier-Stokes Equations with FEMSystem
  2. Nonlinear Elasticity with FEMSystem
  3. Unsteady Linear Elasticity
  4. Mixed-dimension Heat Transfer
  5. Unsteady Linear Elasticity and Isogeometric Analysis (IGA)
• Reduced Basis
  1. Certified Reduced Basis Method
  2. Successive Constraint Method
  3. Transient Reduced Basis Problem
  4. Empirical Interpolation Method
  5. Reduced Cantilever Problem
  6. Heat Transfer on a Curved Domain in 3D
  7. Acoustic Horn
• Adjoints
  1. Adjoint-based Goal Oriented Refinement
  2. Adjoint-based Parameter Sensitivities
  3. Adjoint-based coupled coupled Stokes + Convection Diffusion Goal Oriented Refinement
  4. Adjoint-based Goal Oriented Refinement
  5. SolutionHistory, General Localized Vectors and Unsteady Adjoints
  6. Poisson Equation in square domain with AdjointRefinementErrorEstimator
  7. Unsteady Adjoint Refinement Error Estimator for Model Error Estimation
• Vector-Valued Finite Elements
  1. Uncoupled Poisson Problem
  2. Unsteady Navier-Stokes with FEMSystem
  3. Nedelec Elements for H(curl) Problems in 2D
  4. Nedelec Elements for H(curl) Problems in 3D
  5. Discontinuous Galerkin Vector Poisson Problem
  6. Raviart-Thomas Elements for H(div) Div-Grad Problems in 2D and 3D
  7. Hybridized Raviart-Thomas Elements for Poisson
  8. Hybridized Local Discontinuous Galerkin Elements for Poisson
  9. Hybridized Local Discontinuous Galerkin Elements for Navier-Stokes
  10. Raviart-Thomas Elements for H(div) Grad-Div Problems in 2D and 3D
• Miscellaneous
  1. Infinite Elements for the Wave Equation
  2. Complex Numbers and the "FrequencySystem"
  3. 2D Laplace-Young Problem Using Nonlinear Solvers
  4. Using a Shell Matrix
  5. Interior Penalty Discontinuous Galerkin
  6. Meshing with Triangle and Tetgen
  7. Variational Inequalities and PetscDMNonlinearSolver
  8. Pointcloud-based Meshfree Interpolation
  9. Thermal "film resistance" with an Interface Term
  10. Stitching Meshes
  11. Loop Subdivision Shell Elements
  12. MITC4 Shell Elements
  13. Quad8 Shell Elements
  14. Infinite Elements With Imaginary Frequency
  15. Infinite Elements With Zero Frequency: Unbound Laplace Equation
  16. Static Condensation with Second Order Lagrange Elements
  17. Demonstrating mix of preallocated/hash-table matrix assemblies
• Optimization
  1. Optimization of a Quadratic Objective Function
  2. Constrained Optimization
• Solution Transfer
  1. Transfer Solution From One Mesh to Another