Sequential metric-based adaptive mesh generation

Generating anisotropic meshes translates into generating a mesh in which the desired sizing depends on the direction. In many computational areas including both areas of Finite Elements Analysis and visual graphics, there are cases where the function to be interpolated exhibits high variation in only one direction. For example, meshing the surface of a cylinder with elongated elements aligned with the axis of the cylinder can produce a surface mesh with with high fidelity and low number of elements at the same time. In contrast, creating a surface mesh only with isotropic elements will require a significant higher number of elements in order to achieve the same fidelity. In the context of Computation Fluid Dynamics (CFD) simulations, the traditional approach to simulations is to generate a mesh which will be passed to a solver in order to approximate the solution of the problem. After, a number of iterations the solver will request a new mesh from the mesh generation component while providing information about the error of the solution on the previous mesh. For reasons, similar to the above example it has been found that aligning elements taking into consideration the variation of the solution in each direction can yield a lower interpolation error with fewer elements.