high performance computing on graphics processing units: hgpu.org

Numerical solution models to Maxwell’s equations, which describe electromagnetic wave propagation phenomenon with complete clarity, are of atmost importance in pre-fabrication simulation analyses of the photonic and optoelectronic devices. The Finite Difference Time Domain (FDTD) method, which is based on modeling the differential equations as difference equations in a discretized domain in both space and time, provides for one of the most robust and accurate numerical solution models to Maxwell’s equations. Numerical discretization in cartesian directions, which is most apt for the FDTD method, gives rise to various limitations and errors which need to be analyzed and quantified. The various techniques, to ensure that the limitations are taken care of and the errors bounded, are elaborately studied. Various specific cases of simulation require specific incident wave source and boundary conditions. The various available source and boundary conditions are listed. In case of dispersion, the modeling of waves in dispersive materials requires special techniques like the Auxiliary Differential Equation (ADE) method which is also elaborated. The FDTD simulation is supposed to compute the values of electric and magnetic field components in a domain, given the material properties, wave source conditions and boundary conditions of the domain, and then render the field profile grahics to form videos describing propagation of the fields in the domain. An ideal development environment or combination of development environments to implement FDTD would be one that can perform computations with good speed and accuracy and at the same time offer robust libraries for fast and good quality graphical rendering. Considering the development environments – C (with GNUPLOT graphical libraries), MATLAB and Python, an ideal combination of development environments for FDTD is conclusively arrived at by comparing the speeds of execution and graphical rendering among these development environments in case of a sample two dimensional FDTD simulation. The FDTD method is highly accurate (second order accurate) and extraordinarily uncomplicated (to implement), but at the same time computationally very intensive. The FDTD algorithm is parallelizable and can accomodate hardware acceleration by being parallelized in parallel computing architectures. The NVIDIA Graphical Processing Units (GPUs) are used for this purpose. The FDTD algorithm is not totally parallelizable in terms of NVIDIA GPU architecture. An alternate algorithm of parallelized FDTD to suit the GPU architecture is used. The various specifications and modifications required to be made to the FDTD method to suit a particular problem (even if these problems are related to just one field – Optoelectronics) are vast in number. It is practical to learn the technique of adapting or modifying the algorithm or writing extra logic to suit a particular problem by studying a considerable number of sample scenarios than to make a generic simulation covering every possible scenario. Hence, various specific improvizations and implementations are dealt with, in an attempt to communicate to the Integrated Optoelectronics laboratory, the technique to adapt FDTD to a specific problem, instead of handing over a generic software covering all techniques and explaining the complexitities of its usage.