The research objectives of our group are the design and analysis of numerical methods that can make efficient use of available computational resources by adapting them to data from numerical simulations of predominantly convective processes or to adaptive image and signal processing using multiresolution techniques. The numerical methods for partial differential equations that we design and analyze are used in fields as diverse as gas dynamics (both compressible and incompressible), sedimentation of polydisperse suspensions, flows in porous media, charged particle dynamics, shallow-water models, etc. The ability to use approximation techniques within a multiresolution environment has proven extremely useful in compressing signals with strong gradients in applications such as image restoration, disparity calculations, or optical flow. Specifically designed techniques are also used to preserve other data properties, such as convexity and monotonicity, which is crucial in the data generation process.
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