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Explore advanced quadrature procedures for high-dimensional finite element applications in this 31-minute conference talk from the MFEM Workshop 2025. Delve into the critical but often overlooked aspect of numerical integration in finite element methods, examining various quadrature procedures for both hypercubic and simplicial finite elements. Discover the advantages and disadvantages of different approaches while focusing on unexpected pathologies related to numerical stability and accuracy that emerge in 4D to 7D applications. Learn about the specific challenges and solutions for space-time problems involving three spatial dimensions plus time (3D+t problems) and complex radiation transport problems encompassing three spatial dimensions, three phase-space dimensions, and one temporal dimension (3D+3D+t problems). Gain insights from David Williams of Penn State University as he addresses the importance of proper quadrature selection for large-scale scientific simulations using the MFEM (Modular Finite Element Methods) framework, providing essential knowledge for researchers working with high-order mathematical calculations in multi-dimensional computational domains.
