Domain Decomposition and Model Order Reduction for Electromagnetic Field Simulations in Carbon Fiber Composite Materials

Featured Application: Carbon-fibre-reinforced Polymer (CFRP) is a widely used material in the aerospace industry, but the flaws inside are difficult to detect and may be the cause of failure. This study investigates the simulation of flaw detection at the fibre scale in CFRP using induction thermography to validate the accuracy of this detection. Given the extensive number of unknowns involved in such simulations, one proposes a novel order reduction method combining proper orthogonal decomposition and domain decomposition. Numerical results demonstrate that this approach significantly reduces solution time while maintaining precision. The computation of the electric field in composite materials at the microscopic scale results in an immense number of degrees of freedom. Consequently, this often leads to prohibitively long computation times and extensive memory requirements, making direct computation impractical. In this study, one employs an innovative approach that integrates domain decomposition and model order reduction to retain local information while significantly reducing computation time. Domain decomposition allows for the division of the computational domain into smaller, more manageable subdomains, enabling parallel processing and reducing the overall complexity of the problem. Model order reduction further enhances this by approximating the solution in a lower-dimensional subspace, thereby minimising the number of unknown variables that need to be computed. Comparative analysis between the results obtained from the reduced model and those from direct resolution demonstrates that our method not only reduces computation time but also maintains accuracy. The new method effectively captures the essential characteristics of the electric field distribution in composite materials, ensuring that the local phenomena are accurately represented. This study provides a contribution to the field of computational electromagnetics by presenting a feasible solution to the challenges posed by the high computational demands of simulating composite materials at the microscopic scale. The proposed methodology offers a promising direction for future research and practical applications, enabling more efficient and accurate simulations of complex material systems.