FAU DCN-AvH Seminar: Enriched Finite Elements for Wave Propagation and Heat Diffusion using the Partition of Unity Method

Next Thursday July 11, 2024:

Organized by: FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)

Title: Enriched Finite Elements for Wave Propagation and Heat Diffusion using the Partition of Unity Method
Speaker: M. Shadi Mohamed
Affiliation: Visiting Scientist at FAU DCN-AvH from Heriot-Watt University

Abstract. In this presentation, we discuss the application of the Partition of Unity Finite Element Method (PUFEM) to two challenging types of problems: acoustic wave propagation and heat diffusion in both homogeneous media and functionally graded materials. These problems, while distinct, share a common need for advanced numerical methods due to their inherent complexities.

For acoustic wave problems, maintaining solution accuracy over many wavelengths is critical yet challenging. Traditional finite element methods often struggle with error accumulation, leading to significant inaccuracies and computational infeasibility at high frequencies. PUFEM addresses these challenges by adapting the approximation space to better mimic wave behaviour, thereby reducing error propagation and enhancing computational efficiency.

Heat diffusion problems present a different set of challenges, particularly in materials with poor thermal conductivity or sudden changes in conduction properties. These problems often involve steep temperature gradients and the formation of boundary layers, necessitating highly refined meshes for accurate solutions. PUFEM proves advantageous in these scenarios as well, enabling efficient handling of boundary layers without excessively increasing computational costs.

This presentation showcases PUFEM’s ability to improve the accuracy and efficiency of finite element methods for both acoustic wave and heat diffusion problems while also discussing some of its drawbacks. Hopefully, you will gain insights into how this approach can be applied to your own work, potentially leading to significant improvements in the efficiency of your numerical simulations.

WHEN

Thu. July 11, 2024 at 12:00H

WHERE

On-site: Room 03.323
Friedrich-Alexander-Universität Erlangen-Nürnberg
Cauerstraße 11, 91058 Erlangen
GPS-Koord. Raum: 49.573764N, 11.030028E

Bibliography:
[1] Mohamed, M.S., Seaid, M., Trevelyan, J. and Laghrouche, O., (2013). A partition of unity FEM for time- dependent diffusion problems using multiple enrichment functions. International Journal for Numerical Methods in Engineering, 93(3), pp.245-265.
[2] Drolia, M., Mohamed, M.S., Laghrouche, O., Seaid, M., Trevelyan, J. (2017). Enriched finite elements for initial-value problem of transverse electromagnetic waves in time domain. Computers & Structures, 182, 354-367. [3] Diwan, G.C., Mohamed, M. S. (2019). Pollution studies for high order isogeometric analysis and finite element for acoustic problems. Computer Methods in Applied Mechanics and Engineering, 350, 701-718.
[4] Malek, M., Izem, N., Mohamed, M.S., Seaid, M,, (2020), A three-dimensional enriched finite element method for nonlinear transient heat transfer in functionally graded materials. International Journal of Heat and Mass Transfer 155, 119804.

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