Properties of a Family of Parallel Finite Element Simulations David R. O'Hallaron and Jonathan Richard Shewchuk School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 This report characterizes a family of unstructured 3D finite element simulations that are partitioned for execution on a parallel system. The simulations, which estimate earthquake-induced ground motion in the San Fernando Valley of Southern California, range in size from 10,000--1,000,000 nodes and are partitioned for execution on 4--128 PEs. The purpose of the report is to help researchers better understand the properties of unstructured 3D finite element meshes and the sparse matrix-vector product (SMVP) operations that are induced from them. The report is designed to serve as a comprehensive reference that researchers can consult for answers to the following kinds of questions: For a mesh with a particular number of nodes, how many elements and edges does it have? What is the distribution of node degrees in a 3D mesh? What fraction of nodes in a partitioned mesh are interface nodes? What is the communication volume in a typical parallel SMVP? How many messages are there? How big are the messages? How many nonzeros are contained in the rows of a sparse matrices induced from 3D meshes? The partitioned meshes described in the paper are available electronically. @techreport (sfprops96, author = "D. O'Hallaron and J. Shewchuk" , title = "Properties of a Family of Parallel Finite Element Simulations", institution= "School of Computer Science, Carnegie Mellon University" , number = "CMU-CS-96-141" , year = "1996" , )