ParMooN - a modernized program package based on mapped finite elements

{\sc ParMooN} is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor {\sc MooNMD} \cite{JM04}: strict decoupling of geometry and finite element spaces, implementation of mapped finite elements as their definition can be found in textbooks, and a geometric multigrid preconditioner with the option to use different finite element spaces on different levels of the multigrid hierarchy. After having presented some thoughts about in-house research codes, this paper focuses on aspects of the parallelization for a distributed memory environment, which is the main novelty of {\sc ParMooN}. Numerical studies, performed on compute servers, assess the efficiency of the parallelized geometric multigrid preconditioner in comparison with some parallel solvers that are available in the library {\sc PETSc}. The results of these studies give a first indication whether the cumbersome implementation of the parallelized geometric multigrid method was worthwhile or not.Comment: partly supported by European Union (EU), Horizon 2020, Marie Sk{\l}odowska-Curie Innovative Training Networks (ITN-EID), MIMESIS, grant number 67571

ParMooN - a modernized program package based on mapped finite elements

PARMOON is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor MOONMD [28]: strict decoupling of geometry and finite element spaces, implementation of mapped finite elements as their definition can be found in textbooks, and a geometric multigrid preconditioner with the option to use different finite element spaces on different levels of the multigrid hierarchy. After having presented some thoughts about in-house research codes, this paper focuses on aspects of the parallelization, which is the main novelty of PARMOON. Numerical studies, performed on compute servers, assess the efficiency of the parallelized geometric multigrid preconditioner in comparison with parallel solvers that are available in external libraries. The results of these studies give a first indication whether the cumbersome implementation of the parallelized geometric multigrid method was worthwhile or not

Analyzing object categories via novel category ranking measures defined on visual feature embeddings

Visualizing 2-D/3-D embeddings of image features can help gain an intuitive understanding of the image category landscape. However, popular visualization methods of visualizing such embeddings (e.g. color-coding by category) are impractical when the number of categories is large. To address this and other shortcomings, we propose novel quantitative measures defined on image feature embeddings. Each measure produces a ranked ordering of the categories and provides an intuitive vantage point from which to view the entire set of categories. As an experimental testbed, we use deep features obtained from category-epitomes, a recently introduced minimalist visual representation, across 160 object categories. We embed the features in a visualization friendly yet similarity-preserving 2-D manifold and analyze the inter/intra-category distributions of these embeddings using the proposed measures. Our analysis demonstrates that the category ordering methods enable new insights for the domain of large-category object representations. Moreover, our ordering measure approach is general in nature and can be applied to any feature-based representation of categories