Finite Elements without Meshing

Scan&Solve™ software for engineering analysis from Intact Solutions is based on a patented meshfree technology that liberates Finite Element Analysis (FEA) from the dependence on and limitations of meshing. It has been applied to virtually all types of FEA problems and engineering analysis; example applications include heat transfer, elasticity, plate bending and natural vibration, hydrodynamics, torsion, non-linear and time-varying problems, geometric design (fairing), material modeling, and many more. The salient feature of the technology is separate handling and controls of geometric and physical computational models that are seamlessly combined at solution run time.

The advantages of this approach include unprecedented flexibility in handling geometric errors, small features, complex boundary conditions, and interfaces, while maintaining most of the benefits of classical FEA. Scan&Solve™ can be applied to any geometric model and used within any geometric modeling system that supports two fundamental queries: point membership testing and distance to boundary computation. The white paper describes the technical background behind the Scan&Solve™ technology, summarizes its implementation, and demonstrates its advantages.

Download the white paper here.

Contact us to find out even more about Scan&Solve™ technology or to learn how Scan&Solve can meet your simulation needs.

Mesh-based FEA Compared to Scan&Solve™

Mesh-based FEA Scan&Solve™
Geometry approximated by the mesh of finite elements Native geometry is used
Pre-processing: heuristic simplification and meshing Pre-processing: none
Meshing must resolve all geometric errors and tolerances Geometric errors are irrelevant so long as points can be classified and distances to the boundary can be computed
Mesh size is determined by the smallest feature size Mesh size is determined by the desired resolution of the analysis model (uniform grid)
Small features must be removed Small features are preserved and handled automatically
Boundary conditions: enforced at the nodes only Boundary conditions: enforced on all points of the boundary
Derivatives: pre-computed Derivatives: pre-computed and run-time
Integration: Gauss points of finite elements Integration: Gauss points determined at run-time
Basis functions: local support Basis functions: local support
Sparse linear system Sparse linear system
Geometric accuracy control: fixed and limited by the mesh Geometric accuracy control: determined by accuracy of geometric computations (point test, distance); adaptive
Analysis accuracy control: h-, p-, and k-refinement Analysis accuracy control: h-, p-, and k-refinement