# H-Matrix and Block Error Tolerances

@article{Bradley2011HMatrixAB, title={H-Matrix and Block Error Tolerances}, author={Andrew M. Bradley}, journal={arXiv: Numerical Analysis}, year={2011} }

We describe a new method to map the requested error tolerance on an H-matrix approximation to the block error tolerances. Numerical experiments show that the method produces more efficient approximations than the standard method for kernels having singularity order greater than one, often by factors of 1.5 to 5 and at a lower computational cost.

## 13 Citations

### Improvement of Hierarchical Matrices with Adaptive Cross Approximation for Large-scale Simulation

- Computer ScienceJ. Inf. Process.
- 2015

Application of the proposed method enables us to perform large-scale simulations such that the conventional H-matrices with ACA fail to construct the low-rank approximation, and is confirmed through numerical experiments on an earthquake cycle simulation.

### Implicit level set algorithms for modelling hydraulic fracture propagation

- MathematicsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2016

A class of numerical schemes that have been developed to use the multiscale asymptotic behaviour typically encountered near the fracture boundary as multiple physical processes compete to determine the evolution of the fracture are described.

### Unstructured PEEC formulations considering resistive, inductive and capacitive effects for power electronics

- Computer Science
- 2016

The aim of this thesis is to introduce the capacitive and magnetic effects into the method PEEC to get a general tool, efficient and usable at the industry level, and to enable a simple use of the software InCad3D for non-expert user on numerical methods.

### Pore2Field - Flows and Mechanics in Natural Porous Media from Pore to Field Scale Pore2Field - Physique des écoulements en milieux poreux naturels : de l'échelle du pore à l'échelle du réservoir

- Computer Science
- 2012

Comparing the top two methods, the AGM is preferable over the HEnKF, both when it comes to preserving the initial geology of the ensemble and to the consistency of the predictions.

### Slip-corrected liquid permeability and its effect on hydraulic fracturing and fluid loss in shale

- Geology
- 2015

### Diagnostic fracture-injection tests with complex fracture networks

- Geology
- 2014

Abstract Diagnostic fracture-injection tests (DFIT) are small-volume fracturing tests used to estimate the minimum principal stress and other formation properties. Conventional DFIT interpretation…

### Natural-hydraulic fracture interaction: Microseismic observations and geomechanical predictions

- Geology
- 2014

Natural fractures can reactivate during hydraulic stimulation and interact with hydraulic fractures producing a complex and highly productive natural-hydraulic fracture network. This phenomenon and…

### Stimulation Mechanism and the Direction of Propagation of Microseismicity

- Geology
- 2014

In Enhanced Geothermal Systems (EGS), hydraulic stimulation is used to improve formation permeability, most often in crystalline rock such as granite. The classical concept of hydraulic stimulation…

### Characterizing Hydraulic Fracturing With a Tendency-for-Shear-Stimulation Test

- Geology
- 2014

The classical concept of hydraulic fracturing is that a single, planar, opening mode fracture forms. In recent years, there has been a growing consensus that in many formations, natural fractures…

## References

SHOWING 1-8 OF 8 REFERENCES

### Adaptive Low-Rank Approximation of Collocation Matrices

- Computer ScienceComputing
- 2003

The proposed algorithm which uses the ℋ-matrix format is purely algebraic and relies on a small part of the collocation matrix for its blockwise approximation by low-rank matrices.

### Hybrid cross approximation of integral operators

- Computer ScienceNumerische Mathematik
- 2005

This article uses the -matrix representation that approximates the dense stiffness matrix in admissible blocks by low-rank matrices by a new hybrid algorithm that has the same proven convergence as standard interpolation but also the same efficiency as the (heuristic) adaptive cross approximation (ACA).

### Introduction to Hierarchical Matrices with Applications

- Mathematics, Computer Science
- 2003

### Hierarchical Matrices - A Means to Efficiently Solve Elliptic Boundary Value Problems

- Computer Science, MathematicsLecture Notes in Computational Science and Engineering
- 2008

The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients and presents in full detail the adaptive cross approximation method for the efficient treatment of integral operators with non-local kernel functions.

### Variable Order Panel Clustering

- Computer ScienceComputing
- 2000

A new version of the panel clustering method for a sparse representation of boundary integral equations is presented, which employs more general block partitionings and a variable order of approximation is used depending on the size of blocks.

### Internal deformation due to shear and tensile faults in a half-space

- GeologyBulletin of the Seismological Society of America
- 1992

A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a half-space for both point and finite…

### The Fast Solution of Boundary Integral Equations (Mathematical and Analytical Techniques with Applications to Engineering)

- Mathematics
- 2007

### Adaptive Variable-Rank Approximation of General Dense Matrices

- Computer ScienceSIAM J. Sci. Comput.
- 2007

This paper introduces an algorithm which can construct variable-rank approximations for general matrices without the need of an in-depth analysis of the underlying operators: the matrix is fed into the algorithm, and the algorithm approximates it up to an arbitrary precision.