OpenMP Accelerated Nonlinear Ultrasound Simulations via the Discontinuous Galerkin Method

Nonlinear acoustics simulations, which are essential for applications such as histotripsy and high-intensity focused ultrasound (HIFU), require extensive computational resources. The discontinuous Galerkin (DG) method, which is known for high-order accuracy, geometric flexibility, low dispersion error, and scalability, is well-suited for solving nonlinear acoustic wave equations such as the Westervelt equation. To accelerate these calculations, an approach is presented for simulating nonlinear ultrasound propagation using a two-dimensional (2D) axisymmetric full-wave acoustic model that solves the Westervelt equation with the nodal DG method and OpenMP for CPU-based computer architectures. The details of the model are described, and the OpenMP strategy is analyzed across various scenarios, including lossless, lossy, and shock-capturing cases. Performance evaluations reveal that OpenMP accelerates computations with increasing parallel efficiency as the number of elements increases and the number of threads decreases. The parallel efficiency remains consistent despite the additional computational demands of loss and shock capturing. These findings underscore the effectiveness and scalability of the OpenMP framework for nonlinear ultrasound simulations on CPU-based systems.