An effective and easy-to-build/easy-to-use tool for global optimization. — In many practical applications, it is necessary to solve multimodal optimization problems in which the functional to be minimized has several trapping local minima. From the implementation point of view and given the hectic times we live, often, given the problem, it is necessary to set up the optimization algorithm…

The problem of recovering a two-dimensional function of which the amplitude and the amplitude of the transform are known is a classic problem of optics. The first, simple algorithm to solve this problem is that of Gerchberg and Saxton. It consists in assigning an initial guess to the phase of…

The convention typically adopted by the FFT libraries in the 1D case is that the 0 frequency is positioned at the first element of the output sequence. The successive elements correspond to the increasing “positive” frequencies and, finally, the last elements of the output array contain the increasing negative frequencies…

PyCUDA is a Python programming environment that provides immediate access to NVIDIA’s CUDA parallel computation API. It enables either to insert handcrafted CUDA kernels in a Pythonic computational flow or to perform operations by skipping the programming details of the CUDA kernels and using a high-level pythonic programming style. In…

Before proceeding further, please, take a look at Solving the 1D Wave Equation — Numerical Discretization and Solving the 1D Wave Equation — Python Version. The simulation parameters are the same as those for the Python version: The space-time discretization is performed on the host in the same way…

Before proceeding further, please take a look at the theory at Solving the 1D Wave Equation — Numerical Discretization . In the code, the spatial domain is assumed to be

The wave equation is a second-order, partial differential equation (PDE) in which the unknown u satisfies:

Before proceeding further, please, take a look at Solving the 1D Advection Equation — Numerical Discretization — Leapfrog Approach and Solving the 1D Advection Equation — Python Implementation . The simulation parameters are the same as those for the Python version: The space-time discretization is performed on the host…

Before proceeding further, please take a look at the theory in the story: Solving the 1D Advection Equation — Numerical Discretization — Leapfrog approach. In the code, the spatial domain is assumed to be