The Mathematics Interfaces

The mathematics interfaces are a collection of tools for equation-based modeling and for performing special tasks, rather than for modeling specific physics. These interfaces support several PDE formulations as well as general ways to add ODEs, algebraic equations, other global (space-independent) equations, and curvilinear coordinates.

For a list of the available interfaces found under Mathematics branch () when adding interfaces, including the Names, see Physics Interface Guide.

PDE Interfaces

The PDE Interfaces branch contains Partial Differential Equation (PDE) interfaces for PDEs in coefficient form and general form, and for weak form PDEs on different geometry levels.

These interfaces are for entering PDEs in different forms:

•	Coefficient form, for PDEs conforming to the template explained in The Coefficient Form PDE Interfaces.

•	General form, for conservation laws and PDEs resulting from nonlinear material models. See The General Form PDE Interfaces.

•	Weak form, to use the weak formulation of the PDE for maximum flexibility. See The Weak Form PDE Interfaces.

•	The Wave Form PDE Interface solves PDEs with first-order derivatives in time and space using optimized algorithms with respect to speed and memory consumption.

Except for the Wave Form PDE, the PDE interfaces are available in domains, on boundaries, on edges, and at points. The interfaces for the different equation forms are identical except for the default node on the top geometric entity level. Also see Modeling with PDEs.

Classical PDEs

The Classical PDE Interfaces branch contains some classical PDEs that are special cases of the Coefficient Form PDE: Laplace Equation, Poisson's Equation, Wave Equation, Heat Equation, Helmholtz Equation, and Convection-Diffusion Equation interfaces.

Also see Compact and Standard Notations for Classical PDEs.

ODE and DAE Interfaces

The ODE and DAE Interfaces are used to add global, space-independent equations that can represent additional states. The equations can be ODEs, algebraic equations, DAEs, and transcendental equations, either as global equations or as distributed ODEs/DAEs (on domains, boundaries, edges, or at points). For more information about global equations and ODEs, see Modeling with ODEs and DAEs.

Events Interface

The Events Interface is used to create solver events. An event can be explicit or implicit, and the difference is that for explicit events, you must specify the exact time when the event occurs. When an event occurs, the solver stops and provides a possibility to reinitialize the values of states and dependent variables.

Wall Distance Interface

The Wall Distance Interface solves a modified eikonal equation for computing the distance to walls, which is an important quantity for turbulence modeling in fluid-flow simulations.

Curvilinear Coordinates Interface

Use the Curvilinear Coordinates interface to create a curvilinear coordinate system for defining anisotropic material properties following the shape of a geometric object. Three different methods are available for computing the coordinate system: a diffusion method, an elasticity method, and a flow method. You can also provide user-defined coordinate directions.