1403 Advanced HPC Methods for Eigenvalue Problems and Beyond

  • Ali Hashemian, BCAM - Basque Center For Applied Mathematics
  • David Pardo
  • Victor Calo
  • Carla Manni
  • Quanling Deng

In modern science and engineering, many application problems, such as wave propagation in various media, boil down to eigenvalue problems modeled as partial differential equations. The design of efficient and accurate numerical approximation methods for these eigenvalue problems is of fundamental importance. Research in this area has been very active within the mathematical and engineering community for several decades. The aim of this minisymposium is to bring together experts on the numerical analysis of eigenvalue problems arising in science and engineering. We welcome contributions on advanced numerical algorithms and discretization techniques for solving eigenvalue-related problems.

Relevant topics include, but are not limited to, the following:

• Different types of eigenvalue problems (e.g., linear, quadratic, polynomial, and nonlinear eigenproblems)
• Different algorithms for solving eigenvalue problems (e.g., Jacobi–Davidson, LOBPCG, Krylov-based, and analytical methods)
• Advanced discretization techniques for eigen-analysis based on, e.g., finite element methods (FEM), and isogeometric analysis (IGA) including different refinement techniques
• Employing computational geometry and computer-aided design (CAD) including B-splines, T-splines, and NURBS for eigen-analysis
• Innovative numerical methods such as ones employing artificial intelligence (AI), machine learning, and deep learning methods
• Enhancing the accuracy and efficiency of the eigen-analysis using, e.g., non-standard integration methods, and dispersion-minimizing algorithms
• Vibration analysis in structures, fluids, and in problems concerning the fluid–structure interactions (FSI)
• Stability issues of structures including, e.g., beams and plates in micro/nano scales, functionally graded materials (FGMs), and shape-memory alloys (SMAs)
• Wave propagation problems in homogeneous and heterogeneous media including problem arising in, e.g., acoustics, elastodynamics, and electromagnetics
• Frequency and time-domain response of different types of vibration and wave propagation problems under external excitations
• A priori and a posteriori error analysis and adaptivity.

Ali Hashemian, Basque Center for Applied Mathematics (BCAM), Spain
David Pardo, University of the Basque Country (UPV/EHU), Spain
Victor M. Calo, Curtin University, Australia
Carla Manni, University of Rome Tor Vergata, Italy
Quanling Deng, University of Wisconsin-Madison, USA

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