How can you optimize numerical simulations of vibrations and acoustics?

1 Choose the right model

The first step to optimize your numerical simulations is to choose the right model for your problem. Depending on the frequency range, the geometry, the material properties, and the boundary conditions, you may need to use different types of models, such as finite element, boundary element, or ray tracing models. Each model has its own advantages and limitations, so you should compare and evaluate them based on your objectives and criteria. For example, finite element models are more accurate for low-frequency problems, but they require more mesh elements and computational resources. Boundary element models are more efficient for high-frequency problems, but they may not capture the near-field effects well. Ray tracing models are fast and easy to implement, but they may not account for the wave interference and diffraction phenomena.

2 Refine your mesh

The second step to optimize your numerical simulations is to refine your mesh according to the physics and the geometry of your problem. The mesh is the discretization of your domain into smaller elements that represent the variables and the equations of your model. The quality and the size of your mesh affect the accuracy and the stability of your simulation results. You should use a mesh that is fine enough to capture the relevant features and phenomena of your problem, but not too fine to avoid unnecessary computational costs. You can use adaptive mesh refinement techniques to automatically adjust the mesh density based on the error estimates or the gradients of the solution. You can also use different mesh types, such as structured, unstructured, or hybrid meshes, to suit the shape and the complexity of your domain.

3 Implement parallel computing

The third step to optimize your numerical simulations is to implement parallel computing to speed up your calculations and reduce your memory requirements. Parallel computing is the process of dividing your simulation tasks into smaller subtasks that can be executed simultaneously by multiple processors or cores. This can significantly improve your simulation efficiency and scalability, especially for large-scale or nonlinear problems. You can use different parallel computing methods, such as shared-memory, distributed-memory, or hybrid methods, depending on the architecture and the configuration of your hardware and software. You can also use different parallelization strategies, such as domain decomposition, data decomposition, or task decomposition, to optimize the load balancing and the communication overhead among the processors.

4 Validate and verify your results

The fourth step to optimize your numerical simulations is to validate and verify your results to ensure their accuracy and reliability. Validation is the process of comparing your simulation results with experimental data or analytical solutions to assess their agreement and their uncertainty. Verification is the process of checking your simulation setup and your code to identify and eliminate any errors or bugs that may affect your results. You should perform validation and verification throughout your simulation workflow, not only at the end. You should also use different validation and verification techniques, such as sensitivity analysis, convergence analysis, error estimation, or code testing, to evaluate and improve your simulation quality and robustness.