A localised multiscale technique in boundary element method for acoustic wave model

The classical boundary element method (BEM) has emerged as a powerful alternative to the finite element method particularly in cases where better accuracy is required due to problems such as stress concentration or where the domain extends to infinity. In numerical calculation, the BEM has been widely used to solve acoustic problems since BEM offers excellent accuracy due to the discretization only on the structure's boundaries and easy mesh generation. However, BEM has some disadvantages. It suffers from certain drawbacks in terms of computational efficiency. Since most of the BEM leads to a linear system of equations with dense coefficient matrix, this prevents the BEM from being applied to large-scale problems or highresolution mesh. Due to these disadvantages, according to the acknowledged literature, some researchers use hybrid BEM coupling with other methods to improve the computational efficiency or to improve the computational time. This research uses a different technique from the existing hybrid BEM which will improve both the computational efficiency and time. This study highlights that BEM is less accurate for high gradient problem and consumes more computational time. To overcome this problem, a new technique known as multiscale boundary element method (MBEM) is introduced for solving two dimensional acoustic problems. MBEM is introduced in order to reduce the computation time and improve numerical accuracy using the localised multiscale boundary element method (LMBEM) with the help of the FORTRAN language and parallel routine OpenMP. In addition, the truncated Newton method and Newton interpolation are introduced in this multiscale technique. The multiscale technique produces the results faster because of interpolation and accurate initial guess value in a linear system while the mesh refinement for particular elements based on gradient produces more accurate results. Numerical calculation is given to illustrate the efficiency of the proposed method and the solutions have been validated and compared with the BEM. The results show that the MBEM is indeed faster than BEM, with the computational time reduction is almost 33.01%. When the 38 elements are solved using LMBEM, it is more accurate as it gives an average error that is almost similar to a ratio of 38:36 with the 1024 elements using MBEM and BEM. In addition, this research is solving the problem on the boundary. It is suggested that the current study be expanded to solve the problem for the internal nodes of the domain since the internal node value is needed

Diffuse Optical Imaging with Ultrasound Priors and Deep Learning

Diffuse Optical Imaging (DOI) techniques are an ever growing field of research as they are noninvasive, compact, cost-effective and can furnish functional information about human tissues. Among others, they include techniques such as Tomography, which solves an inverse reconstruction problem in a tissue volume, and Mapping which only seeks to find values on a tissue surface. Limitations in reliability and resolution, due to the ill-posedness of the underlying inverse problems, have hindered the clinical uptake of this medical imaging modality. Multimodal imaging and Deep Learning present themselves as two promising solutions to further research in DOI. In relation to the first idea, we implement and assess here a set of methods for SOLUS, a combined Ultrasound (US) and Diffuse Optical Tomography (DOT) probe for breast cancer diagnosis. An ad hoc morphological prior is extracted from US B-mode images and utilised for the regularisation of the inverse problem in DOT. Combination of the latter in reconstruction with a linearised forward model for DOT is assessed on specifically designed dual phantoms. The same reconstruction approach with the incorporation of a spectral model has been assessed on meat phantoms for reconstruction of functional properties. A simulation study with realistic digital phantoms is presented for an assessment of a non-linear model in reconstruction for the quantification of optical properties of breast lesions. A set of machine learning tools is presented for diagnosis breast lesions based on the reconstructed optical properties. A preliminary clinical study with the SOLUS probe is presented. Finally, a specifically designed deep learning architecture for diffusion is applied to mapping on the brain cortex or Diffuse Optical Cortical Mapping (DOCM). An assessment of its performances is presented on simulated and experimental data

Computational Engineering

The focus of this Computational Engineering Workshop was on the mathematical foundation of state-of-the-art and emerging finite element methods in engineering analysis. The 52 participants included mathematicians and engineers with shared interest on discontinuous Galerkin or Petrov-Galerkin methods and other generalized nonconforming or mixed finite element methods

Institute for Computational Mechanics in Propulsion (ICOMP)

The Institute for Computational Mechanics in Propulsion (ICOMP) is operated by the Ohio Aerospace Institute (OAI) and the NASA Lewis Research Center in Cleveland, Ohio. The purpose of ICOMP is to develop techniques to improve problem-solving capabilities in all aspects of computational mechanics related to propulsion. This report describes the accomplishments and activities at ICOMP during 1993

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

JST-SPH: a total Lagrangian, stabilised meshless methodology for mixed systems of conservation laws in nonlinear solid dynamics

The combination of linear finite elements space discretisation with Newmark family time-integration schemes has been established as the de-facto standard for numerical analysis of fast solid dynamics. However, this set-up suffers from a series of drawbacks: mesh entanglements and elemental distortion may compromise results of high strain simulations; numerical issues, such as locking and spurious pressure oscillations, are likely to manifest; and stresses usually reach a reduced order of accuracy than velocities. Meshless methods are a relatively new family of discretisation techniques that may offer a solution to problems of excessive distortion experienced by linear finite elements. Amongst these new methodologies, smooth particles hydrodynamics (SPH) is the simplest in concept and the most straightforward to numerically implement. Yet, this simplicity is marred by some shortcomings, namely (i) inconsistencies of the SPH approximation at or near the boundaries of the domain; (ii) spurious hourglass-like modes caused by the rank deficiency associated with nodal integration, and (iii) instabilities arising when sustained internal stresses are predominantly tensile. To deal with the aforementioned SPH-related issues, the following remedies are hereby adopted, respectively: (i) corrections to the kernel functions that are fundamental to SPH interpolation, improving consistency at and near boundaries; (ii) a polyconvex mixed-type system based on a new set of unknown variables (p, F, H and J) is used in place of the displacementbased equation of motion; in this manner, stabilisation techniques from computational fluid dynamics become available; (iii) the analysis is set in a total Lagrangian reference framework. Assuming polyconvex variables as the main unknowns of the set of first order conservation laws helps to establish the existence and uniqueness of analytical solutions. This is a key reassurance for a robust numerical implementation of simulations. The resulting system of hyperbolic first order conservation laws presents analogies to the Euler equations in fluid dynamics. This allows the use of a well-proven stabilisation technique in computational fluid dynamics, the Jameson Schmidt Turkel (JST) algorithm. JST is very effective in damping numerical oscillations, and in capturing discontinuities in the solution that would otherwise be impossible to represent. Finally, we note that the JST-SPH scheme so defined is employed in a battery of numerical tests, selected to check its accuracy, robustness, momentum preservation capabilities, and its viability for solving larger scale, industry-related problems