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Computational Engineering

The AICES Graduate School focuses on challenging aspects of computational modeling and analysis in the application areas considered: Mathematics, Computer Science, Physics, Mechanical, Electrical, and Civil Engineering, Medicine as well as Georesources and Materials Engineering. This broad spectrum provides fertile ground for targeted research on broadly defined inverse problems.

1. Numerical analysis

Numerical analysis plays a major role at AICES. Focus areas are discretization methods for partial differential equations (PDE) and related fields, such as fast iterative solvers, preconditioning methods, and adaptive methods. Another major research theme is given by discrete and continuous optimization, including research on PDE-constraint optimization, and deterministic global optimization. In the context of control and optimization methods, an important field of research at AICES is model order reduction, such as reduced basis methods for parameterized PDE.

2. Scientific and High-Performance Computing

The emphasis is on the development of algorithms and tools for the whole range of parallel computers, including multicore, accelerated, distributed, and hybrid platforms, as offered by the Rechenzentrum at RWTH and the Jülich Supercomputing Center. On the one hand, AICES provides critical building blocks for large scale simulations: geometric algorithms for data processing and acquisition, algorithmic differentiation, domain-specific compilers, and high-performance linear algebra libraries. On the other hand, AICES focuses on interactive and 3D visualization, computer vision and image synthesis, as well as on programming tools for the generation, analysis, and optimization of parallel codes.

3. Computational Modeling

Modeling provides a mathematical and algorithmic formulation describing a given scientific problem. For complex problems, suitable models often include several submodels that describe aspects of the problem. At AICES, modeling research covers a wide range of techniques, including both discrete methods, like molecular dynamics and quantum mechanics, and continuum methods, like fluid and solid mechanics, thermodynamics and transport problems. These are generally characterized by strong nonlinearities, leading to many challenges, such as non-uniqueness, bifurcation, and instability. Both strong-form and weak-form descriptions are considered. Efficient computational descriptions require different spatial and temporal discretization approaches, based on finite-difference or finite-element schemes. Efficiency can also be increased by using reduced-order models. AICES also applies and refines modeling approaches for surface mechanisms, multi-scale and multi-field problems, constrained problems, inverse problems and optimization problems.

4. Inverse Problems

Inverse problems determine or optimize system inputs and parameters, and other system characteristics using observations of outputs of real systems or the desired specifications of engineered systems. Inverse problems describe many topics, where computational approaches can lead to breakthroughs in design quality, efficiency of operation,and performance of engineered solutions. In this context, numerical simulation no longer replaces the more traditional experimental or analytical methods, but becomes instead a new tool that can discover and identify models for complex phenomena and processes. AICES is advancing computational engineering science in three critical areas of synthesis: model identification supported by model based experimentation, understanding scale interaction and scale integration, and optimal design and operation of engineered systems.

5. Computational Materials Science

Computational materials science models the structure, properties, and behavior of materials. Current work at AICES includes molecular simulations of interfaces and energy-related systems, phase-field modeling of microstructures, multiscale modeling of contact, radiation transport, and group contribution methods. Research at Jülich and Düsseldorf complements work at RWTH, studying biomaterials, structure-property relationships in alloys and magnetic materials, and eigensolvers for density-functional theory. Many problems also require coupling methods to study the full range of material interactions, and close collaboration with experimentalists In addition, since many CMS applications demand significant high-performance computing resources, development of more accurate and efficient algorithms and analysis tools is an active component of CMS research at AICES.

6. Computational Biology

Understanding the cooperation of countless proteins, genes, and other biological entities is crucial for further success in biomedicine. Available data is usually extremely high-dimensional and associated with varying levels of control in biological systems. These problems can be mathematically formulated as inverse problems requiring novel combinations of machine learning, multi-scale modeling, and model order reduction techniques. Examples of current research includes assessing induced pluripotent stem cells by analyzing genome-wide expression patterns (www.pluritest.org), genetic biomarkers for assessing drug action in cancer cell lines, tracking of the dynamics of cellular differentiation or disease propagation, and optimal schemes for insulin dosing. Using a combination of atomistic and coarse-grained modeling, it is possible to explore the relationship between molecular structure and biological processes such as self-assembly and aggregation, which play an important role in many diseases.