Abstract We present an algorithm for hp -adaptive collocation-based mesh-free numerical analysis of partial differential equations. Our solution procedure follows a well-established iterative solve–estimate–mark–refine paradigm. The solve phase relies on the Radial Basis Function-generated Finite Differences (RBF-FD) using point clouds generated by advancing front node positioning that supports...

ABSTRACT We extend the state-of-the-art N-body code pkdgrav3 with inclusion of mesh-free gas hydrodynamics for cosmological simulations. Two new hydrodynamic solvers have been implemented, mesh-less finite volume and mass methods. The manifestly conserve mass, momentum, energy, validated a wide range standard test simulations, including also describe improvements to that implemented performing ...

This work presents a high-accuracy, mesh-free, generalized Stokes theorem-based numerical quadrature scheme for integrating functions over trimmed parametric surfaces and volumes. The algorithm relies on two fundamental steps: (1) We iteratively reduce the dimensionality of integration using theorem to line integrals trimming curves, (2) we employ antidifferentiation in high-order rules. achiev...

Mesh plays an indispensable role in dense realtime reconstruction essential in robotics. Efforts have been made to maintain flexible data structures for 3D data fusion, yet an efficient incremental framework specifically designed for online mesh storage and manipulation is missing. We propose a novel framework to compactly generate, update, and refine mesh for scene reconstruction upon a volume...