Topic
Irregular matrix
About: Irregular matrix is a research topic. Over the lifetime, 23 publications have been published within this topic receiving 221 citations.
Papers
TL;DR: In this paper, the shape factor of Kazemi et al. (1992) was shown to be exact under pseudo-steady-state conditions within the dual continuum mathematical concept of natural fractured dual porosity systems.
Abstract: Kazemi et al. (SPE Reserv Eng 7(2):219–227, 1992) suggested an empirical matrix-fracture transfer function, verified based on experimental data of Mattax and Kyte (Trans AIME 225(15):177–184, 1962), to model fluid flow in naturally fractured dual porosity petroleum reservoirs using a dual-porosity numerical simulator. Their generalized shape factor should be valid for all possible irregular matrix blocks. The factor is calculated based on the volume of the matrix block, the surface open to flow in all directions and the distances of these surfaces to the centre of the matrix block. The summation is done over all open surfaces of a matrix block. Kazemi et al. (1992) showed that for rectangles and cylinders the formula reduces to the well-known forms of the shape factor. By the time, many authors indicated the validity of the formula, but no theoretical proof was offered for that so far. This study derives the Kazemi et al. (1992) shape factor using control volume finite difference discretization on the fracture-matrix dual continuum. The matrix blocks are handled as Voronoi polyhedra. The derivation is given for both isotropic and tensorial matrix permeability. Based on this derivation the authors conclude that the Kazemi et al. (SPE Reserv Eng 7(2):219–227, 1992) formula is exact under pseudo-steady-state conditions within the dual continuum mathematical concept of natural fractured dual porosity systems.
41 citations
TL;DR: In this paper, a stochastic particle tracking method for complex fracture networks with irregular matrix blocks is proposed. But the method does not take into account the matrix effect without mesh generation.
Abstract: [1] Particle-tracking methods are often used to model contaminant transport in fractured porous media because they are straightforward to implement for fracture networks and are able to take into account the matrix effect without mesh generation. While classical methods assume infinite matrix or regularly spaced fractures, we have developed a stochastic method adapted to solute transport in complex fracture networks associated with irregular matrix blocks. Diffusion times in the matrix blocks are truncated by the finite size of the blocks. High ratios of matrix diffusion to fracture advection, small fracture apertures, and small blocks favor the transfer of particles to nearby fractures through matrix diffusion. Because diffusion occurs on both sides of the originating fracture before particles reach one of the neighboring fractures, transfer times to both neighboring fractures are strongly affected by the network configurations on both sides of the fracture. This new particle-tracking method is able to deal with complex fracture networks by considering heterogeneous configurations on both sides of the fracture. We finally show on simple Sierpinski lattice structures that neglecting the finite size of the matrix blocks may lead to orders of magnitude overestimations of the transfer times.
39 citations
TL;DR: In this article, a task-based formulation of Scalable Universal Matrix Multiplication Algorithm (SUMMA) is applied to the multiplication of hierarchy-free, rank-structured matrices that appear in the domain of quantum chemistry (QC).
Abstract: A task-based formulation of Scalable Universal Matrix Multiplication Algorithm (SUMMA), a popular algorithm for matrix multiplication (MM), is applied to the multiplication of hierarchy-free, rank-structured matrices that appear in the domain of quantum chemistry (QC). The novel features of our formulation are: (1) concurrent scheduling of multiple SUMMA iterations, and (2) fine-grained task-based composition. These features make it tolerant of the load imbalance due to the irregular matrix structure and eliminate all artifactual sources of global synchronization.Scalability of iterative computation of square-root inverse of block-rank-sparse QC matrices is demonstrated; for full-rank (dense) matrices the performance of our SUMMA formulation usually exceeds that of the state-of-the-art dense MM implementations (ScaLAPACK and Cyclops Tensor Framework).
31 citations
TL;DR: In this paper, the stiffness matrices of a large group of repeated and regular structures were obtained using graph products, considering the importance of increasing the speed of constructing the structure and reducing the complexity.
Abstract: The inverse of the stiffness matrices of a large group of repeated and regular structures were previously obtained using graph products. Considering the importance of increasing the speed o...
19 citations
TL;DR: In this paper, an irregular matrix model which has and Virasoro symmetry is presented, which is obtained using the colliding limit of the Toda field theories and produces the inner product between irregular modules of symmetry.
Abstract: We present an irregular matrix model which has and Virasoro symmetry. The irregular matrix model is obtained using the colliding limit of the Toda field theories and produces the inner product between irregular modules of symmetry. We evaluate the partition function using the flow equation which is the realization of Virasoro and symmetry.
15 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 1 |
| 2018 | 1 |
| 2017 | 2 |
| 2016 | 4 |
| 2015 | 5 |
| 2014 | 1 |