An accurate and effective computational method to solve brain tumor problems: a Jacobian-free Newton Krylov method with an innovative preconditioning strategy II

Brain glioma, a highly debilitating brain tumor, poses significant challenges for medical professionals and researchers globally due to its complex progression and invasive nature. Despite advancements in surgery, radiotherapy, and chemotherapy, glioblastoma multiform (GBM) remains notably resistant to treatment. Recent studies highlight the efficacy of the chemotherapy agent Temozolomide (TMZ) in enhancing survival rates, particularly when combined with radiotherapy. However, the optimal sequencing and combination of these treatments remain under investigation. Mathematical modeling has emerged as a powerful tool to simulate glioma behavior and optimize treatment strategies. These models incorporate biological principles, clinical data, and treatment parameters, using reaction-diffusion equations to replicate tumor growth dynamics. This paper explores the application of sophisticated mathematical and computational models to simulate the interplay between radiotherapy, chemotherapy, and glioma progression, aiming to develop optimized treatment strategies. By employing the Jacobian-free Newton Krylov (JFNK) method and an innovative physics-based preconditioning technique, we demonstrate computational accuracy and efficiency that improve treatment optimization. Our findings emphasize the potential of these models to enhance therapeutic outcomes for GBM patients.