We propose a simple level set method for the Dirichlet k-partition problem which aims to partition an open domain into K different subdomains as minimize sum of smallest eigenvalue Laplace operator in each subdomain. first formulate nested minimization functional function and eigenfunction defined As approximation, we simply replace by so that can then be converted single problem. apply standar...

Since the seminal work of Idelsohn, O\~nate and Del-Pin (2004), Particle Finite Element Method (PFEM) has relied on a Delaunay triangulation Alpha--Shape (AS) algorithm in remeshing process. This approach guarantees good quality Lagrangian mesh, but introduces list shortcomings that demand geometrical treatments tailored to each problem. In order improve process PFEM, this proposes use Level--S...

We present a novel interface-capturing scheme, THINC-scaling, to unify the VOF (volume of fluid) and level set methods, which have been developed as two different approaches widely used in various applications. The key success is maintain high-quality THINC reconstruction function using field accurately retrieve geometrical information fulfill numerical conservativeness. interface well defined ...