Meshfree Methods: A Speedy Approach to Complex Simulations

As the clock was ticking down, it became clear that speed was the name of the game when it came to tackling complex simulations. With only three days left until departure and two of those days falling on Labor Day weekend, our team had to get up to speed quickly.

In this regard, meshfree methods have proven to be a valuable tool for tackling challenging problems. One such method is the Local Maximum-Entropy Approximation Scheme, which uses genetic algorithms to ensure accurate results. Another approach is the RBF Meshless Method, which has been successfully applied to injection molding modeling.

For simulations that require strain smoothing and regularization, Galerkin meshfree methods can be stabilized using this technique. Additionally, the Fuzzy Grid Method offers a powerful tool for solving Lagrangian gas dynamics equations.

When dealing with arbitrary discontinuities, new shape functions have been developed that eliminate the need for additional unknowns. The Meshless BEM has also proven effective in 2-D stress analysis of linear elastic functionally graded materials.

In another innovation, the Particle-Partition of Unity Method has been adapted to incorporate adaptivity. This technique has been used to simulate complex problems involving moving interfaces.

For high-dimensional Fokker-Planck equations, deterministic particle methods have shown promise. Bridging Scale Method and its applications offer a further tool for tackling challenging simulations.

A New Stabilized Nodal Integration Approach has also been developed, which combines well with the Finite Pointset Method for incompressible flows. Assessment of generalized finite elements in nonlinear analysis is another area where meshfree methods are being applied.

In addition, a meshfree method has been used to simulate interactions between fluids and flexible structures. Goal-oriented error estimation for the Element Free Galerkin Method has also been developed, providing an additional level of accuracy.

Finally, bubble and Hermite natural element approximations have been explored as further alternatives for complex simulations.

By leveraging these innovative meshfree methods, our team was able to quickly get up to speed and deliver accurate results within a tight deadline.

Meshfree methods lectures