Boundary element methods for the wave equation based on hierarchical matrices and adaptive cross approximation

Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices have to be computed for a large number of time steps or frequencies. In this article, we propose a new approximation scheme for the Convolution Quadrature Method powered BEM, which we apply to scattering problems governed by the wave equation. We use $${\mathscr {H}}^2$$ H 2 -matrix compression in the spatial domain and employ an adaptive cross approximation algorithm in the frequency domain. In this way, the storage and computational costs are reduced significantly, while the accuracy of the method is preserved.

Machine Learning to Design an Auto-tuning System for the Best Compressed Format Detection for Parallel Sparse Computations

Many applications in scientific computing process very large sparse matrices on parallel architectures. The presented work in this paper is a part of a project where our general aim is to develop an auto-tuner system for the selection of the best matrix compression format in the context of high-performance computing. The target smart system can automatically select the best compression format for a given sparse matrix, a numerical method processing this matrix, a parallel programming model and a target architecture. Hence, this paper describes the design and implementation of the proposed concept. We consider a case study consisting of a numerical method reduced to the sparse matrix vector product (SpMV), some compression formats, the data parallel as a programming model and, a distributed multi-core platform as a target architecture. This study allows extracting a set of important novel metrics and parameters which are relative to the considered programming model. Our metrics are used as input to a machine-learning algorithm to predict the best matrix compression format. An experimental study targeting a distributed multi-core platform and processing random and real-world matrices shows that our system can improve in average up to 7% the accuracy of the machine learning.

A fast and oblivious matrix compression algorithm for Volterra integral operators

The numerical solution of dynamical systems with memory requires the efficient evaluation of Volterra integral operators in an evolutionary manner. After appropriate discretization, the basic problem can be represented as a matrix-vector product with a lower diagonal but densely populated matrix. For typical applications, like fractional diffusion or large-scale dynamical systems with delay, the memory cost for storing the matrix approximations and complete history of the data then becomes prohibitive for an accurate numerical approximation. For Volterra integral operators of convolution type, the fast and oblivious convolution quadrature method of Schädle, Lopez-Fernandez, and Lubich resolves this issue and allows to compute the discretized evaluation with N time steps in $O(N \log N)$ O ( N log N ) complexity and only requires $O(\log N)$ O ( log N ) active memory to store a compressed version of the complete history of the data. We will show that this algorithm can be interpreted as an ${{\mathscr{H}}}$ H -matrix approximation of the underlying integral operator. A further improvement can thus be achieved, in principle, by resorting to ${{\mathscr{H}}}^{2}$ H 2 -matrix compression techniques. Following this idea, we formulate a variant of the ${{\mathscr{H}}}^{2}$ H 2 -matrix-vector product for discretized Volterra integral operators that can be performed in an evolutionary and oblivious manner and requires only O(N) operations and $O(\log N)$ O ( log N ) active memory. In addition to the acceleration, more general asymptotically smooth kernels can be treated and the algorithm does not require a priori knowledge of the number of time steps. The efficiency of the proposed method is demonstrated by application to some typical test problems.

Steady-State Gas Flow from Tight Shale Matrix Subject to Water Blocking

Summary This work studies 1D steady-state flow of gas from compressible shale matrix subject to water blocking toward a neighboring fracture. Water blocking is a capillary end effect causing wetting phase (e.g., water) to accumulate near the transition from matrix to fracture. Hydraulic fracturing is essential for economical shale gas production. Water is frequently used as fracturing fluid, but its accumulation in the matrix can reduce gas mobility and production rate. Gas transport is considered at a defined pressure drop. The model accounts for apparent permeability (slip), compressibility of gas and shale, permeability reduction, saturation tortuosity (reduced relative permeability upon compaction), and multiphase flow parameters like relative permeability and capillary pressure, which depend on wettability. The behavior of gas flow rate and distributions of gas saturation, pressure, and permeability subject to different conditions and the stated mechanisms is explored. Water blockage reduces gas relative permeability over a large zone and reduces the gas flow rate. Despite gas flowing, strong capillary forces sustain mobile water over the entire system. Reducing drawdown gave lower driving force and higher resistance (by water blockage) for gas flow. The results show that 75% reduction of drawdown made the gas flow rate a couple orders of magnitude lower compared to if there was no blockage. The impact was most severe in more water-wetsystems. The blockage caused most of the pressure drop to occur near the outlet. High pressure in the rest of the system reduced effects from gas decompression, matrix compression, and slip-enhanced permeability, whereas rapid gradients in all these effects occurred near the outlet. Gas decompression resulted in an approximately 10 times higher Darcy velocity and pressure gradient near the outlet compared to inlet, which contributed to removing blockage, but the added resistance reduced the gas production rate. Similarly, higher gas Corey exponent associated gas flow with higher pressure drop. The result was less blockage but lower gas production. Slip increased permeability, especially toward the outlet, and contributed to increase in gas production by 16%. Significant matrix compression was associated with permeability reduction and increased Corey exponent in some examples. These effects reduced production and shifted more of the pressure drop toward the outlet. Upstream pressure was more uniform, and less compression and permeability reduction were seen overall compared to a system without water blockage.

Extracellular matrix compression temporally regulates microvascular angiogenesis

Mechanical cues influence tissue regeneration, and although vasculature is known to be mechanically sensitive, little is known about the effects of bulk extracellular matrix deformation on the nascent vessel networks found in healing tissues. Previously, we found that dynamic matrix compression in vivo potently regulated revascularization during bone tissue regeneration; however, whether matrix deformations directly regulate angiogenesis remained unknown. Here, we demonstrated that load initiation time, magnitude, and mode all regulate microvascular growth, as well as upstream angiogenic and mechanotransduction signaling pathways. Immediate load initiation inhibited angiogenesis and expression of early sprout tip cell selection genes, while delayed loading enhanced microvascular network formation and upstream signaling pathways. This research provides foundational understanding of how extracellular matrix mechanics regulate angiogenesis and has critical implications for clinical translation of new regenerative medicine therapies and physical rehabilitation strategies designed to enhance revascularization during tissue regeneration.

Guidelines and Limitations of the Compact Compression Specimen

Damage initiation and propagation material models for carbon fiber composites can be categorized according to the loading applied to constituent components. An example of such categorization is fiber tension, fiber compression, matrix tension, and matrix compression material models. Of these, matrix compression has been by far the least studied based on amount of published literature. Recent work at Oregon State University (OSU) has begun to address this lack of study. OSU researchers have published several papers culminating in the specification of an effective test specimen for isolating matrix compression damage initiation and propagation in carbon fiber laminates. While providing compelling results indicating the effectiveness and usefulness of this test specimen, little or no information has been provided regarding its manufacture, usable notch lengths, and optimum loading rate during testing. Experience at OSU has shown that this information is critical and not trivial to obtain. The purpose of this paper is to provide specific guidelines and “lessons learned” needed for other researchers to efficiently and effectively use this specimen in a comprehensive study. Test specimens are manufactured in the OSU Composites Materials Manufacturing Laboratory using typical commercial pre-peg carbon fiber following the specified layup and curing procedures. Once the material was cured the carbon fiber plate was then water-jet cut into the desired geometry and notch length. Usable notch length and optimum loading rate was determined by testing a series of specimens. All testing was conducted at an OSU lab using a universal testing machine with Digital Image Correlation (DIC) data collected. Specimens were preloaded and matrix compression initiation and propagation data collected until tensile failure occurred on the back edge of the specimen. Testing showed that shorter notch lengths result in inconsistent data and longer in effective initiation but limited propagation due to reduced ligament length. Testing suggested that a speed less than 5 mm/min gave the best results as faster displacement rates caused less crack propagation to occur, while increasing the likelihood of the specimen to fail in tension along its back edge. Through the use of these guidelines, researchers are able to manufacture and use an effective test specimen for the investigation of matrix compression damage initiation and propagation.