Rodin::Adaptation module

Mesh adaptation and deformation operations.

\[ \mathbf{x}^{\prime}=\mathbf{x}+\mathbf{d}(\mathbf{x}). \]

SWIFT::Adapt and SWIFT::Problem fit mesh interfaces to level sets while controlling element distortion. DeformationMap and CellDeformation describe mapped geometry for evaluating deformed cells and fields. These components support moving-interface calculations and body-fitted mesh updates.

Design

The module follows a strict separation of concerns:

  • The level set $ \phi $ owns the topology of the tracked domain ( $ \phi < 0 $ inside, $ \phi > 0 $ outside).
  • Classification converts $ \phi $ into discrete cell attributes (see Geometry utilities such as the min s-t cut classifier).
  • Geometry fitting (SWIFT) moves and curves the mesh. It never decides topology.

The SWIFT step solves a metric-preconditioned (natural-gradient) problem built entirely in the variational form language: a surface force (the Welsch first variation, assembled on interface facets) balanced against fitting and centered distribution metrics. Affine quadratic hinges recover quality in the direction problem. Hard admissibility (element validity) is enforced by a nonlinear line search.

Key classes

  • Parameters — budgets, tolerances and weights
  • Report — per-solve diagnostics
  • Problem — local fitting without mesh mutation
  • Adapt — owned P1 setup and in-place displacement

Representative formula

SWIFT combines fitting and distribution contributions in the displacement metric:

\[ M=F+D. \]

The metric acts on displacement directions; admissibility is checked during line search. See SWIFT for the fitting model and contracts.

Namespaces

namespace SWIFT
Robust interface fitting with a fitting–distribution metric.

Classes

class CellDeformation
Lazily evaluated deformation state of a mesh cell.
template<class Displacement, class LocatorType>
class DeformationMap
The deformation $\Phi(x)=x+u(x)$ induced by a displacement.