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
• Transient Systems
  1. Solving a Transient Linear System in Parallel
  2. The Newmark System and the Wave 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?
• Subdomains
  1. Solving on a Subdomain
  2. Subdomain-Restricted Variables
• FEMSystem Framework
  1. Unsteady Navier-Stokes Equations with FEMSystem
  2. Nonlinear Elasticity with FEMSystem
• 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
• 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
• Vector-Valued Finite Elements
  1. Uncoupled Poisson Problem
  2. Unsteady Navier-Stokes with FEMSystem
• 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. Pointclould-based Meshfree Interpolation