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Applied and Computational Mathematics

In our group of applied and computational mathematics (anvendt og beregningsorientert matematikk, ABM), important research areas are: hydrodynamics and ocean modeling, industrial mathematics and reservoir simulations, image processing, geometric integration and scientific computing.

The need for using mathematics and computations to solve fundamental problems in science, technology, medicine, industry, is strongly increasing. By a combination of experiments, observations, theory development, modeling and numerical simulations, it is possible to gain deeper insight into complicated processes. Numerical computations have been important for many years in fields of mathematics, physics and geology; however, also  subjects like biology, chemistry, geology and medicine are becoming increasingly dependent on mathematical modelling and simulations.

To participate actively to this development, it is important that UiB has a strong research group in applied and computational mathematics, and that mathematicians and researchers from other disciplines come together for collaboration and progress.

  • Applied Analysis

    The activities of this group are focused on mathematical and numerical analysis of ordinary and partial differential equations. Main research topics are wave-type equations such as KdV and nonlinear Schrödinger, analysis of Hele-Shaw flows, and analysis of spectral methods. Another important topic is the analysis of level set methods for image reconstruction.

  • Energy surface for 2 parameters quantum gates

    Computational Quantum Physics

    Electrons are so small and their movement so fast that we cannot follow their movement with instruments. On this scale (nanometres), strange things happen that can no longer be described by Newton's laws. This is the reality of Quantum Mechanics....

  • Numerisk simulering av nordlyset

    Geometric Integration

    Numerical integration of differential equations is a research area within Numerical Analysis, with the goal of devising good numerical methods to compute the time evolution of systems of differential equations. This is an important issue in all simulations of dynamical systems and physical processes.

  • Internal waves in the Indian Ocean

    Hydrodynamics

    The Hydrodynamics group carries out analytical and numerical studies of waves and currents. A portion of the activity is aimed at obtaining a fundamental understanding of how, for example, waves occur, propagate and break.

  • ingressbilde

    Images and Signals

    Digital images are "mosaics" where the pieces (called pixels) are so small that they cannot be seen individually by the naked eye. These mosaic tiles are represented in the computer as numbers, which, with the help of mathematical methods, can tell us much more than the eye can. This field is called digital image processing.

  • plasma

    Mechanics, dynamical systems and modelling

    In this specialisation within applied and computational mathematics, the main emphasis is placed on the modelling in time and space of large numbers of "particles" that interact with each other and with the environment.

  • ingressbilde

    Nonlinear Waves

    Research in nonlinear waves includes the study of surface water waves, internal waves, CO2 storage, and other mathematical problems in fluid mechanics, such as the stability of coherent structures. Techniques used include complete integrability, analysis of differential equations, and numerical simulation.

  • Reservoir Group

    The Reservoir Group educates students and researchers in the basic challenges associated with solving the equations that describe flow and transport in porous media. These include the development of rigorous mathematical foundations for the empirical physical laws of fluid motion in porous media, numerical methods for solving the partial differential equations that arise, and characterisation of reservoir properties via inverse modelling based on the observed production history of a reservoir.