Publications by Giacomo Rosilho De Souza

Optimal explicit stabilized postprocessed τ-leap method for the simulation of chemical kinetics

The simulation of chemical kinetics involving multiple scales constitutes a modeling challenge (from ordinary differential equations to Markov chains) and a computational challenge (multiple scales, large dynamical systems, time step restrictions). In this ...

Academic Press Inc Elsevier Science2023

Explicit Stabilized Multirate Method For Stiff Stochastic Differential Equations

Assyr Abdulle, Giacomo Rosilho De Souza

Stabilized explicit methods are particularly efficient, for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they lose their efficiency when a severe stiffness is induced by very few "fast" de ...

SIAM PUBLICATIONS2022

Explicit Stabilized Multirate Method For Stiff Differential Equations

Assyr Abdulle, Giacomo Rosilho De Souza

Stabilized Runge???Kutta methods are especially efficient for the numerical solution of large systems of stiff nonlinear differential equations because they are fully explicit. For semi-discrete parabolic problems, for instance, stabilized Runge???Kutta me ...

AMER MATHEMATICAL SOC2022

Mixed-precision explicit stabilized Runge-Kutta methods for single- and multi-scale differential equations

Giacomo Rosilho De Souza, Matteo Croci

Mixed-precision algorithms combine low-and high-precision computations in order to benefit from the performance gains of reduced-precision without sacrificing accuracy. In this work, we design mixed-precision Runge-Kutta-Chebyshev (RKC) methods, where high ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

A local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations

Assyr Abdulle, Giacomo Rosilho De Souza

We introduce a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations. The proposed method is based on a coarse grid and iteratively improves the solution's accuracy by solving local elliptic problems in refined subdomains ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Numerical methods for deterministic and stochastic differential equations with multiple scales and high contrasts

Giacomo Rosilho De Souza

Mathematical models involving multiple scales are essential for the description of physical systems. In particular, these models are important for the simulation of time-dependent phenomena, such as the heat flow, where the Laplacian contains mixed and ind ...

EPFL2020

A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

Assyr Abdulle, Giacomo Rosilho De Souza

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic problems in high gra ...

EDP SCIENCES S A2019