Abstract The simplest restricted three-body problem, in which two massive points and a massless point particle attract one another according to Newton’s law of inverse squares, has pulsating Hill’s regions where the moves inside closed surrounding only points. Until now, no numerical integrator is known maintain these regions, making it challenging reproduce phenomenon gravitational capture par...

The paper studies several approaches to numerical integration over a domain defined implicitly by an indicator function such as the level set function. The integration methods are based on subdivision, moment–fitting, local quasi-parametrization and Monte-Carlo techniques. As an application of these techniques, the paper addresses numerical solution of elliptic PDEs posed on volumetric domains ...

The paper studies several approaches to numerical integration over a domain defined implicitly by an indicator function such as the level set function. The integration methods are based on subdivision, moment–fitting, local quasi-parametrization and Monte-Carlo techniques. As an application of these techniques, the paper addresses numerical solution of elliptic PDEs posed on domains and manifol...