Mesh, offline data, and time integration

Collaboration diagram for Mesh, offline data, and time integration:

Classes
class	ryujin::Discretization< dim >
class	ryujin::MeshAdaptor< dim, Number >
class	ryujin::OfflineData< dim, Number >
class	ryujin::AssemblyScratchData< dim >
class	ryujin::AssemblyCopyData< dim, Number >
class	ryujin::TimeIntegrator< dim, Number >
class	ryujin::TransfiniteInterpolationManifold< dim, spacedim >

Enumerations
enum class	ryujin::MeshType { ryujin::MeshType::serial , ryujin::MeshType::parallel_shared , ryujin::MeshType::parallel_distributed , ryujin::MeshType::parallel_fullydistributed }
enum class	ryujin::AdaptationStrategy { ryujin::AdaptationStrategy::global_refinement , ryujin::AdaptationStrategy::random_adaptation , ryujin::AdaptationStrategy::smoothness_indicators }
enum class	ryujin::MarkingStrategy { ryujin::MarkingStrategy::fixed_threshold }
enum class	ryujin::TimePointSelectionStrategy { ryujin::TimePointSelectionStrategy::fixed_time_points , ryujin::TimePointSelectionStrategy::simulation_cycle }
enum class	ryujin::CFLRecoveryStrategy { ryujin::CFLRecoveryStrategy::none , ryujin::CFLRecoveryStrategy::bang_bang_control , ryujin::CFLRecoveryStrategy::cruise_control }
enum class	ryujin::TimeSteppingScheme {   ryujin::TimeSteppingScheme::ssprk_22 , ryujin::TimeSteppingScheme::ssprk_33 , ryujin::TimeSteppingScheme::erk_11 , ryujin::TimeSteppingScheme::erk_22 ,   ryujin::TimeSteppingScheme::erk_33 , ryujin::TimeSteppingScheme::erk_43 , ryujin::TimeSteppingScheme::erk_54 , ryujin::TimeSteppingScheme::strang_ssprk_33_cn ,   ryujin::TimeSteppingScheme::strang_erk_33_cn , ryujin::TimeSteppingScheme::strang_erk_43_cn , ryujin::TimeSteppingScheme::imex_11 , ryujin::TimeSteppingScheme::imex_22 ,   ryujin::TimeSteppingScheme::imex_33 }

Detailed Description

The Discretization class holding the triangulation and finite element, the OfflineData class holding the precomputed matrices and sparsity patterns, the MeshAdaptor, and the TimeIntegrator (include/ryujin/discretization).

Enumeration Type Documentation

MeshType

enum class ryujin::MeshType

strong

An enum class for setting the type of Triangulation that should be constructed.

Enumerator
serial	Use serial dealii::Triangulation<dim>
parallel_shared	Use parallel dealii::parallel::shared::Triangulation<dim>
parallel_distributed	Use parallel dealii::parallel::distributed::Triangulation<dim>
parallel_fullydistributed	Use parallel dealii::parallel::fullydistributed::Triangulation<dim>

Definition at line 31 of file discretization.h.

AdaptationStrategy

enum class ryujin::AdaptationStrategy

strong

Controls the spatial mesh adaptation strategy.

Enumerator
global_refinement	Perform a uniform global refinement.
random_adaptation	Perform random refinement and coarsening with a deterministic Mersenne Twister and a chosen seed. This refinement strategy is only useful for debugging and testing.
smoothness_indicators	Perform local refinement and coarsening based on smoothness indicators.

Definition at line 26 of file mesh_adaptor.h.

MarkingStrategy

enum class ryujin::MarkingStrategy

strong

Controls the marking strategy used for mesh adaptation. This configuration option is ignored for the uniform global refinement strategy.

Enumerator
fixed_threshold	Refine and coarsen according to a fixed tolerance normalized according to the difference between the maximal and minimal attained values for the chosen refinement indicators.

Definition at line 52 of file mesh_adaptor.h.

TimePointSelectionStrategy

enum class ryujin::TimePointSelectionStrategy

strong

Controls the time point selection strategy.

Enumerator
fixed_time_points	Perform a mesh adaptation cycle at preselected fixed time points.
simulation_cycle	Perform a mesh adaptation cycle at every nth simulation cycle.

Definition at line 66 of file mesh_adaptor.h.

CFLRecoveryStrategy

enum class ryujin::CFLRecoveryStrategy

strong

Controls the chosen invariant domain / CFL recovery strategy.

Enumerator
none	Step with the chosen "cfl max" value and do nothing in case an invariant domain and or CFL condition violation is detected.
bang_bang_control	Step with the chosen "cfl max" value and, in case an invariant domain or "CFL condition" violation is detected, the time step is repeated with "cfl min". If this is unsuccessful as well, a warning is emitted.
cruise_control	Adaptive strategy that similarly to "bang bang control" first steps with the chosen "cfl max" value, and, in case of an invariant domain violation or a "CFL condition" violation restarts the time step using a tau_max hint coming from the sub step where we encountered a problem. This is the default strategy.

Definition at line 28 of file time_integrator.h.

TimeSteppingScheme

enum class ryujin::TimeSteppingScheme

strong

Controls the chosen time-stepping scheme.

Enumerator
ssprk_22	The strong stability preserving Runge Kutta method of order 2, SSPRK(2,2;1/2), with the following butcher tableau \begin{align*} \begin{array}{c|ccc} 0 & 0 \\ \tfrac{1}{2} & \tfrac{1}{2} & 0 \\ \hline 1 & 1 & 0 \end{array} \end{align*}
ssprk_33	The strong stability preserving Runge Kutta method of order 3, SSPRK(3,3;1/3), with the following butcher tableau \begin{align*} \begin{array}{c|ccc} 0 & 0 \\ 1 & 1 & 0 \\ \tfrac{1}{2} & \tfrac{1}{4} & \tfrac{1}{4} & 0\\ \hline 1 & \tfrac{1}{6} & \tfrac{1}{6} & \tfrac{2}{3} \end{array} \end{align*}
erk_11	The explicit Runge-Kutta method RK(1,1;1), aka a simple, forward Euler step.
erk_22	The explicit Runge-Kutta method RK(2,2;1) with the butcher tableau \begin{align*} \begin{array}{c|ccc} 0 & 0 \\ \tfrac{1}{2} & \tfrac{1}{2} & 0 \\ \hline 1 & 0 & 1 \end{array} \end{align*}
erk_33	The explicit Runge-Kutta method RK(3,3;1) with the butcher tableau \begin{align*} \begin{array}{c|ccc} 0 & 0 \\ \tfrac{1}{3} & \tfrac{1}{3} & 0 \\ \tfrac{2}{3} & 0 & \tfrac{2}{3} & 0 \\ \hline 1 & \tfrac{1}{4} & 0 & \tfrac{3}{4} \end{array} \end{align*}
erk_43	The explicit Runge-Kutta method RK(4,3;1) with the butcher tableau \begin{align*} \begin{array}{c|ccc} 0 & 0 \\ \tfrac{1}{4} & \tfrac{1}{4} & 0 \\ \tfrac{1}{2} & 0 & \tfrac{1}{2} & 0 \\ \tfrac{3}{4} & 0 & \tfrac{1}{4} & \tfrac{1}{2} & 0 \\ \hline 1 & 0 & \tfrac{2}{3} & -\tfrac{1}{3} & \tfrac{2}{3} \end{array} \end{align*}
erk_54	The explicit Runge-Kutta method RK(5,4;1) with the butcher tableau TODO
strang_ssprk_33_cn	A Strang split using ssprk 33 for the hyperbolic subproblem and Crank-Nicolson for the parabolic subproblem
strang_erk_33_cn	A Strang split using erk 33 for the hyperbolic subproblem and Crank-Nicolson for the parabolic subproblem
strang_erk_43_cn	A Strang split using erk 43 for the hyperbolic subproblem and Crank-Nicolson for the parabolic subproblem
imex_11	A Euler IMEX splitting. This is the low order IMEX method: it performs a forward Euler time step for the hyperbolic subproblem and then a backward Euler time step for the parabolic subproblem.
imex_22	A second order implicit-explicit method. It uses the explicit midpoint rule with Butcher tableau \begin{align*} \begin{array}{c|ccc} 0 & 0 \\ \tfrac{1}{2} & \tfrac{1}{2} & 0 \\ 1 & 0 & 1 & 0 \end{array} \end{align*} to solve the hyperbolic subproblem, and a two-stage Crank-Nicolson type diagonally implicit Runge-Kutta scheme with Butcher tableau \begin{align*} \begin{array}{c|ccc} 0 & 0 \\ \tfrac{1}{2} & 0 & \tfrac{1}{2} \\ 1 & \tfrac{1}{2} & \tfrac{1}{2} & 0 \end{array} \end{align*} to solve the parabolic subproblem. Each of the two stages consists of one explicit hyperbolic step and one implicit parabolic step with step size \(\tau / 2\).
imex_33	The third order implicit-explicit method IMEX(3, 3; 1), see [7], Section 4.3. It uses Heun's third order explicit Runge-Kutta scheme with Butcher tableau \begin{align*} \begin{array}{c|cccc} 0 & 0 \\ \tfrac{1}{3} & \tfrac{1}{3} & 0 \\ \tfrac{2}{3} & 0 & \tfrac{2}{3} & 0 \\ 1 & \tfrac{1}{4} & 0 & \tfrac{3}{4} & 0 \end{array} \end{align*} to solve the hyperbolic subproblem, and a three-stage diagonally implicit Runge-Kutta scheme with Butcher tableau \begin{align*} \begin{array}{c|cccc} 0 & 0 \\ \tfrac{1}{3} & \tfrac{1}{3} - \gamma & \gamma \\ \tfrac{2}{3} & \gamma & \tfrac{2}{3} - 2 \gamma & \gamma \\ 1 & \tfrac{1}{4} & 0 & \tfrac{3}{4} & 0 \end{array} \end{align*} with \(\gamma = \tfrac{1}{2} + \tfrac{1}{2\sqrt{3}}\) to solve the parabolic subproblem. Each of the three stages consists of one explicit hyperbolic step and one implicit parabolic step with step size \(\tau / 3\).

Definition at line 59 of file time_integrator.h.