Integration of different classes of numerical techniques, optimization algorithms and Monte Carlo simulation. Improving performance of numerical algorithms in general by means of parallel and distributed computing for multi-core architectures, distributed systems, utilizing both CPU and GPU, new CPU/GPU hybrid architectures.

Finding plausible mathematical models with intuitive control which capture the reflectance properties of real-world materials. Photorealistic rendering based on sound mathematical models. Methods for texture representation and robust interpolation in the context of GPU real-time rendering of 2D/3D graphics. Real-time scientific visualization.

Robust and fast methods for acquiring real-world data and detecting its dominating features, crucial in forming the data, from the images. Modeling the data to reflect their fundamental properties by means of geometric stochastic processes with intuitive set of parameters.

Developing robust and general numerical methods for modeling high intensity light propagation through highly nonlinear media and active photonics devices. Incorporating multi-photon processes into propagation model for polymers and semiconductor quantum dots.