ModelW

ModelW is intended for wave-propagation PDE systems. It uses the same packed state layout as ModelD, but the auxiliary block satisfies a time-dependent equation.

Canonical system:

\[ \frac{\partial q}{\partial t} + \nabla u = 0, \]

\[ \frac{\partial u}{\partial t} + \nabla \cdot F(u,q,w,v,x,t;\mu) = S(u,q,w,v,x,t;\mu). \]

In preprocessing, ModelW sets tdep = 1, wave = 1, nc = ncu * (nd + 1), and ncq = ncu * nd.

Difference From ModelD

ModelD uses \(q + \nabla u = 0\) as an algebraic mixed relation. ModelW uses \(\partial q/\partial t + \nabla u = 0\), so the q block is part of the time-evolved wave state.

Required And Optional Functions

For frontend-generated models, define:

• initu for the initial u state.
• initq for the initial q state.
• initw for wave examples that use w; the current MATLAB/Julia generation paths expect initw for ModelW.
• mass to generate Tdfunc when time dependence is active.

Text2Code uses the corresponding Initu, Initq or Inituq, Initw, and Tdfunc functions.

Representative Examples

Example	u	q	Notes
Acoustic wave	Pressure-like variable	Velocity/gradient-like wave variable	First-order acoustic system.
Elastic wave	Displacement/stress-related variables	Velocity/gradient-like variables	Depends on chosen first-order form.
Electromagnetic wave	Field component block	Companion wave block	User supplies Maxwell-type fluxes.
General wave system	Primary wave variables	Time-evolved auxiliary block	Requires consistent initu and initq.

Repository examples include examples/WaveEquation/Membrane and examples/WaveEquation/Scattering.

When To Choose ModelW

Choose ModelW when:

• The model is fundamentally a first-order wave system.
• The q block is not just a recovered gradient.
• You need explicit initial conditions for both u and q.

Do not choose ModelW solely because the problem is time dependent. Many time-dependent diffusion and flow problems are still ModelD or ModelC.