Listing of documented examples

About the examples

Source code for these examples can be found in Sundance/examples. The doxygen pages linked here will show a short description of the main() function. To see a source browser page, follow the link "Go to the source code for this file."

Laplace's equation

This example shows many of the core features of Sundance in the context of a simple linear PDE: getting a Mesh, defining geometry regions via CellFilter objects, setting up a weak form and boundary conditions using Expr objects, forming a LinearProblem, getting the solution back as a DiscreteFunction (a subtype of Expr), and then postprocessing and output. This example is explained in detail in the document GettingStarted.pdf.

Laplace3D.cpp

Infrastructure

These examples show the skeleton of "boilerplate" code that appears in most simulations you'll develop, as well as utilities for user input via command-line options and parameter lists. These examples are explained in detail in the document GettingStarted.pdf.

Boilerplate code: Skeleton.cpp
Defining command-line options: CommandLineOptions.cpp
Reading Teuchos::ParameterList objects from XML files: XMLParameterList.cpp

Linear PDE

Solve a system of two coupled PDEs: Coupled2D.cpp.
How to use a single LinearProblem to do multiple solves of a PDE over a range of parameter values: ParameterSweep.cpp
How to do a mixed discretization: TaylorHoodStokes2D.cpp
Nitsche's boundary condition method: NitschePoisson2D.cpp
Vorticity-streamfunction formulation of Stokes' equation: VorticityStokes2D.cpp
Block preconditioning for Stokes' equation: PCDStokesCouette2D.cpp
Loose coupling of heat transport and fluid flow: CoolingIdealFlow.cpp.

Nonlinear PDE

These examples solve Bratu's equation $-\nabla^2 u = \lambda e^u + f$ using several different methods. These examples are explained in detail in the document NonlinearExamples.pdf.

Fixed-point iteration: FixedPointBratu1D.cpp
Newton's method with linearization done by hand and a simple user-level Newton loop: HandLinearizedNewtonBratu1D.cpp
Newton's method with the linearization automated, but the Newton loop still done at the user level: AutoLinearizedNewtonBratu1D.cpp
Newton's method with the linearization automated and the solve done by a packaged Newton-Armijo algorithm (Playa or NOX): FullyAutomatedNewtonBratu1D.cpp. In most cases this is the most efficient and robust way to program a nonlinear PDE.
An outer loop with continuation on the parameter $\lambda$ : ContinuationBratu1D.cpp. A single nonlinear problem object is reused for every continuation step, similar to how a single linear problem was used through the sweep in ParameterSweep.cpp.

Transient PDE

Crank-Nicolson stepping for the heat conduction equation in 2D: TransientHeat2D.cpp
Crank-Nicolson stepping for the radiation diffusion equation in 1D: TransientNonlinear1D.cpp.
Crank-Nicolson stepping for radiation diffusion equation in 1D, with automatic stepsize control: StepControlledTransientNonlinear1D.cpp.