• Corpus ID: 238634363

Cost of space-time formulations: a study on the performance of direct and iterative solvers on space-time formulations versus time-marching schemes

  title={Cost of space-time formulations: a study on the performance of direct and iterative solvers on space-time formulations versus time-marching schemes},
  author={Marcin Skotniczny and Anna Paszynska and Maciej Paszyński},
We focus on finite element method computations for time-dependent problems. We prove that the computational cost of the space-time formulation is higher than the cost of the time-marching schemes. This applies to both direct and iterative solvers. It concerns both uniform and adaptive grids. The only exception from this rule is the h adaptive space-time simulation of the traveling point object, resulting in refinements towards their trajectory in the space-time domain. However, if this object… 


Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids
The quality of the orderings found by the heuristic algorithm to construct element partition trees are compared to those generated by alternative state-of-the-art algorithms and show 50% reduction in flops number and execution time.
Quasi-Optimal Elimination Trees for 2D Grids with Singularities
This work proposes a heuristic construction of the elimination trees that has cost O(Ne log(Ne), where Ne is the number of elements in the mesh, and shows that this heuristic ordering has similar computational cost to the quasi-optimal elimination trees found with dynamic programming and outperforms state-of-the-art alternatives in the authors' numerical experiments.
Volume and neighbors algorithm for finding elimination trees for three dimensional h-adaptive grids
Hierarchical Matrices: Algorithms and Analysis
This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g.,
Computational Complexity of Hierarchically Adapted Meshes
We show that for meshes hierarchically adapted towards singularities there exists an order of variable elimination for direct solvers that will result in time complexity not worse than
The Multifrontal Method for Sparse Matrix Solution: Theory and Practice
This paper presents an overview of the multifrontal method for the solution of large sparse symmetric positive definite linear systems. The method is formulated in terms of frontal matrices, update
Iterative methods for sparse linear systems
This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
This work presents a new coarsening heuristic (called heavy-edge heuristic) for which the size of the partition of the coarse graph is within a small factor of theSize of the final partition obtained after multilevel refinement, and presents a much faster variation of the Kernighan--Lin (KL) algorithm for refining during uncoarsening.