Developments in Numerical Methods for Complex Systems

The field of numerical methods for complex systems is moving towards the development of more efficient and accurate techniques for solving coupled problems. Researchers are focusing on creating high-order methods that can handle complex geometries and nonlinearities, with a emphasis on stability, convergence, and computational efficiency. The use of adaptive sampling procedures, hyperreduction, and novel finite element methods are being explored to improve the performance of reduced-order models and computational simulations. These advancements have the potential to significantly impact various fields, including aerodynamics, hydrodynamics, and geotechnical engineering. Noteworthy papers include: A high-order combined interpolation/finite element technique for evolutionary coupled groundwater-surface water problems, which demonstrates unconditionally stable and temporally second-order accurate results. A polyhedral scaled boundary finite element method for three-dimensional seepage analysis, which achieves higher accuracy and faster convergence compared to conventional FEM.

Sources

A high-order combined interpolation/finite element technique for evolutionary coupled groundwater-surface water problem

A Goal-Oriented Adaptive Sampling Procedure for Projection-Based Reduced-Order Models with Hyperreduction

On the one-dimensional SPH approximation of fractional-order operators

Three dimensional seepage analysis using a polyhedral scaled boundary finite element method

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