4 papers
Jacobi Hamiltonian Integrators: construction and applications
Adérito Araújo, Gonçalo Inocêncio Oliveira, João Nuno Mestre
We propose a systematic framework for constructing geometric integrators for Hamiltonian systems on Jacobi manifolds. By combining Poissonization of Jacobi structures with homogene…
Optimal error estimates for a discontinuous Galerkin method on curved boundaries with polygonal meshes
Adérito Araújo, Milene Santos
We consider a discontinuous Galerkin method for the numerical solution of boundary value problems in two-dimensional domains with curved boundaries. A key challenge in this setting…
Jacobi Hamiltonian Integrators
Adérito Araújo, Gonçalo Inocêncio Oliveira, João Nuno Mestre
We develop a method of constructing structure-preserving integrators for Hamiltonian systems in Jacobi manifolds. Hamiltonian mechanics, rooted in symplectic and Poisson geometry,…
The infinite partition of a line segment and multifractal objects
A. I. L. de Araújo, R. F. Soares, J. P. de Oliveira +1
We report an algorithm for the partition of a line segment according to a given ratio . At each step the length distribution among sets of the partition follows a binomial distr…