Academic Aims

academic aims

Computational engineering plays a central role in process and product design, production planning, and operations, while computational science has joined the analytical and experimental avenues of investigation as a widely-accepted third pillar of scientific inquiry. The following development trends are currently apparent: an increasing intricacy of the physical or engineering systems being analyzed (complexity), a growing range of interacting scales which must be considered at once (multiscale), larger numbers of interacting physical phenomena that are inseparable (multiphysics), and, demands for best-design identification with reduced input from human intuition (optimization). To address these challenges, the graduate school sets out to advance computational engineering science primarily in the critical area of synthesis. Here objectives often share a common trait, in that they are examples of broadly-defined inverse problems. Such problems are conceptually different from direct analysis problems that have been the cornerstone of science and engineering for centuries. In direct computational analysis problems, the system output is determined as a result of given system characteristics and inputs, in direct analogy to an experimental analysis. In inverse problems on the other hand, system inputs, system parameters, or any other internal characteristics of the system are determined on the basis of observations and measurements of outputs of a real system or of the given specifications of an engineered system with desired properties. In model identification problems, either some characteristics of (at least) one of the models, or model interaction mechanism, are yet to be determined, and the computational analysis is performed repeatedly while the results are compared against either experimental data, or computational results obtained with a more fundamental (and presumably more compute-intensive) model. In systems design problems, other aspects of the system are sought, e.g., network structure, geometrical shape or time-varying control profiles, and the computations are iteratively repeated while comparing the results against some measure of system performance. It is important to note that, while direct problems can be addressed with or without modeling and computation by mere experimentation and measurement, models and computational methods are a crucial element of inverse problems, as they, loosely speaking, connect measured output data to input data or systems characteristics that cannot be accessed directly in the course of the experiments.

The areas of expertise of the principal investigators form the initial group of AICES research topics. This list is classified in three categories below, and is by no means closed.

1. Applications and Models

  • Materials engineering: solidification and design of metal forming processes
  • Chemical engineering: modeling and integrated design of product and process systems
  • Transportation: aircraft design and automotive engine design
  • Electrical engineering: electrical machines, communications, semiconductors
  • Biology and medicine: cardiovascular, respiratory and cellular systems
  • Geoscience: geological reservoirs and processes in the Earth

2. Mathematical and Numerical Methods

  • Robust discretization, stabilized and anisotropic finite elements, finite volume methods
  • Adaptive multi-resolution methods and multilevel solvers
  • Optimization methods
  • Model identification and model-based experimental design methods
  • Deforming-domain flow simulation and grid moving techniques
  • Fluid-structure coupling and associated conservation properties
  • Averaging and closure techniques
  • Model reduction: singular limits, asymptotic and multiscale methods
  • Generation, optimization and parametrization of geometric representations

3. Computational Tools and Infrastructure

  • Parallel computing on shared memory, distributed-memory and hybrid architectures
  • Data and model management and modeling support tools 
  • Multiphysics simulation tools 
  • Automatic differentiation 
  • Immersive visualization 
  • Performance tools