Note that contrary to Gmsh, VTK supports exclusively Lagrange polynomials and ParaView provides uniform h-refinement to visualize these polynomials. Although it has not been tested yet within this work, this new feature opens up additional promising perspectives for the visualization of high-order meshes and solutions. Recently, the support for arbitrary-order Lagrange polynomials has also been introduced in ParaView. Consequently, memory requirement can be significantly reduced for the selective h-refinement procedure compared to uniform h-refinement. In the second case, recursive h-refinements is applied to the parent elements and their child elements until this error is locally minimized. The recursive h-refinement of the initial mesh which generates the visualization grid can be either uniform (every edge of the parent element is split in the same way) or selective, based on a local visualization error. Afterwards, traditional visualization of the solution occurs through a straightforward piecewise linear interpolation on the Then, the high-order polynomial solution is interpolated on the new nodes of the refined visualization grid. First, a recursive h-refinement of high-order elements based on classical automatic mesh refinement (AMR) is applied and defines a refined linear visualization grid. The visualization capabilities of Gmsh rely on a two-step strategy further described in. This allows to encode any polynomial basis using the same framework. ![]() Moreover, a major asset of the native file format of Gmsh consists in the use of an explicit description of the polynomial basis functions within the file, instead of an imposed convention. Historically, few open source tools provide high-order meshing and visualization capabilities. 1 – Illustration of the usage of the GmshReader plugin in ParaView. ![]() This coupling enables parallel visualization of massive high-order solution in parallel, in client-server mode.įig. This plugin combines respectively ParaView’s scalability in parallel and Gmsh’s ability to apply h-refinement of the initial mesh followed by the interpolation of any arbitrary high-order polynomial solutions on the resulting visualization grid. In this context, a new ParaView plugin which integrates Gmsh as an external library has been implemented for off-line post-processing and visualization of high-order solutions saved under the Gmsh format, see Figure 1. ![]() Only very recently, arbitrary-order Lagrange polynomials have been introduced in VTK and their support in ParaView for both high-order meshes and solutions is gaining traction, which confirms the growing interest and need for such features. However, ParaView relies on the Visualization Toolkit (VTK) whose data models have historically mainly supported linear elements. On the other hand, ParaView is an efficient open source parallel visualization tool which has been used successfully for post hoc visualization of large scale, unstructured data sets up to several billions of dof. However, Gmsh is in essence a serial tool and is therefore limited to a relatively low number of dof and level of h-refinements. The high-order solution is then interpolated at the new mesh nodes in order to provide an optimal visualization grid. This method relies on recursive h-refinements of the initial mesh, coupled to a projection error estimation. The open source mesh and visualization tool Gmsh provides a general method for the post-processing of high-order finite element fields. ![]() However, the lack of visualization tools able to handle a large number of degrees of freedom (dof) has been a major bottleneck for the analysis of high-order finite element solutions generated by massively parallel simulations. Recently high-order finite element methods initially introduced in the research community such as discontinuous Galerkin (DG) and flux reconstruction (FR) have gained considerable attention in industry, thanks to their high-accuracy on unstructured meshes, their efficiency and scalability.
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