Graphical processing units (GPUs) promise to revolutionize scientific computing in the near future. Already, they allow almost real-time integration of simplified numerical models of cardiac tissue dynamics. However, the integration methods that have been developed so far are typically of low order and use single precision arithmetics. In this work, we describe numerical implementation of […]

September 9, 2013 by hgpu

## GPU-based parallel solver via the Kantorovich theorem for the nonlinear Bernstein polynomial systems

This paper proposes a parallel solver for the nonlinear systems in Bernstein form based on subdivision and the Newton-Raphson method, where the Kantorovich theorem is employed to identify the existence of a unique root and guarantee the convergence of the Newton-Raphson iterations. Since the Kantorovich theorem accommodates a singular Jacobian at the root, the proposed […]

January 13, 2012 by hgpu

The Arnold diffusion constitutes a dynamical phenomenon which may occur in the phase space of a non-integrable Hamiltonian system whenever the number of the system degrees of freedom is M>=3. The diffusion is mediated by a web-like structure of resonance channels, which penetrates the phase space and allows the system to explore the whole energy […]

December 3, 2011 by hgpu

In this study, chaotic partial differential equations (PDEs) were numerically solved using a parallel algorithm on graphics processing units (GPU). This new method will aid in our search for simple examples of chaotic PDEs. Computational time using the GPU was compared to other languages such as Matlab and PowerBASIC. The GPU algorithm was optimized using […]

December 1, 2011 by hgpu

The Arnold diffusion constitutes a dynamical phenomenon which may occur in the phase space of a non-integrable Hamiltonian system whenever the number of the system degrees of freedom is $M geq 3$. The diffusion is mediated by a web-like structure of resonance channels, which penetrates the phase space and allows the system to explore the […]

July 22, 2011 by hgpu