Taylor-Series Expansion Based Numerical Methods: A Primer, Performance Benchmarking and New Approaches for Problems with Non-smooth Solutions

in Archives of Computational Methods in Engineering (2019)

We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these ... [more ▼]

We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files including input files, boundary conditions, point distribution and solution fields, so as to facilitate future benchmarking of new methods. We review traditional methods and recent ones which appeared in the last decade. We aim to help newcomers to the field understand the main characteristics of these methods and to provide sufficient information to both simplify implementation and benchmarking of new methods. Some of the examples are chosen within a subset of problems where collocation is traditionally known to perform sub-par, namely when the solution sought is non-smooth, i.e. contains discontinuities, singularities or sharp gradients. For such problems and other simpler ones with smooth solutions, we study in depth the influence of the weight function, correction function, and the number of nodes in a given support. We also propose new stabilization approaches to improve the accuracy of the numerical methods. In particular, we experiment with the use of a Voronoi diagram for weight computation, collocation method stabilization approaches, and support node selection for problems with singular solutions. With an appropriate selection of the above-mentioned parameters, the resulting collocation methods are compared to the moving least-squares method (and variations thereof), the radial basis function finite difference method and the finite element method. Extensive tests involving two and three dimensional problems indicate that the methods perform well in terms of efficiency (accuracy versus computational time), even for non-smooth solutions. [less ▲]

Temperature Fields Induced by Low Power Focused Ultrasound in Soft Tissues During Gene Therapy. Numerical Predictions and Experimental Results

in Archives of Acoustics (2009), 34(4), 445459

Textual Inference with Deep Learning Technique

in Proceedings of the 28th Annual Benelux Conference on Artificial Intelligence (BNAIC2016). (2016)

Thermo-mechanical coupling and part-level analysis for additive manufacturing processes

Scientific Conference (2021, January 13)

[1] Hussein, A. and Hao, L. and Yan, C. and Everson, R. Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting. Materials & Design ... [more ▼]

[1] Hussein, A. and Hao, L. and Yan, C. and Everson, R. Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting. Materials & Design (1980-2015), (2013), 52:638–647. [2] Bangerth, W. and Hartmann, R. and Kanschat, G. deal.II – a General Purpose Object Oriented Finite Element Library. ACM Trans. Math. Softw.(2007), Vol. 33., 4:24/1–24/27. [less ▲]

Thermodynamically constrained averaging theory for cancer growth modelling

in IFAC-PapersOnLine (2016), 49(26), 289-294

In Systems Biology, network models are often used to describe intracellular mechanisms at the cellular level. The obtained results are difficult to translate into three-dimensional biological systems of ... [more ▼]

In Systems Biology, network models are often used to describe intracellular mechanisms at the cellular level. The obtained results are difficult to translate into three-dimensional biological systems of higher order. The multiplicity and time dependency of cellular system boundaries, mechanical phenomena and spatial concentration gradients affect the intercellular relations and communication of biochemical networks. These environmental effects can be integrated with our promising cancer modelling environment, that is based on thermodynamically constrained averaging theory (TCAT). Especially, the TCAT parameter viscosity can be used as critical player in tumour evolution. Strong cell-cell contacts and a high degree of differentiation make cancer cells viscous and support compact tumour growth with high tumour cell density and accompanied displacement of the extracellular material. In contrast, dedifferentiation and losing of cell-cell contacts make cancer cells more fluid and lead to an infiltrating tumour growth behaviour without resistance due to the ECM. The fast expanding tumour front of the invasive type consumes oxygen and the limited oxygen availability behind the invasive front results automatically in a much smaller average tumour cell density in the tumour core. The proposed modelling technique is most suitable for tumour growth phenomena in stiff tissues like skin or bone with high content of extracellular matrix. [less ▲]

Three-Dimensional Crack Propagation with Global Enrichment XFEM and Vector Level Sets

Scientific Conference (2015)

Three-dimensional non-linear fracture mechanics by enriched meshfree methods without asymptotic enrichment

in Proceedings of the IUTAM Symposium on Discretization Methods for Evolving Discontinuities (2007)

This paper presents a three-dimensional, extrinsically enriched meshfree method for initiation, growth and coalescence of an arbitrary number of cracks in non-linear solids including large deformations ... [more ▼]

This paper presents a three-dimensional, extrinsically enriched meshfree method for initiation, growth and coalescence of an arbitrary number of cracks in non-linear solids including large deformations, for statics and dynamics. The novelty of the methodology fashioned in this work is that only an extrinsic discontinuous enrichment and no near-tip/asymptotic enrichment is required. Instead, a Lagrange multiplier field is added along the crack front to close the crack along the front. This decreases the computational cost and removes difficulties involved with a branch enrichment. Numerical examples treated include the pull-out of a reinforcement bar from a concrete block, and a Taylor bar impact with very large deformation and fragmentation. The results are compared to experimental results, and other simulations from the literature, which shows the robustness and accuracy of the method. © 2007 Springer. [less ▲]

Time and frequency domain analysis of piezoelectric energy harvesters by monolithic finite element modeling

in International Journal for Numerical Methods in Engineering (2017)

The successful design of piezoelectric energy harvesting devices relies upon the identification of optimal geometrical and material configurations to maximize the power output for a specific band of ... [more ▼]

The successful design of piezoelectric energy harvesting devices relies upon the identification of optimal geometrical and material configurations to maximize the power output for a specific band of excitation frequencies. Extendable predictive models and associated approximate solution methods are essential for analysis of a wide variety of future advanced energy harvesting devices involving more complex geometries and material distributions. Based on a holistic continuum mechanics modeling approach to the multi-physics energy harvesting problem, this article proposes a monolithic numerical solution scheme using a mixed-hybrid 3-dimensional finite element formulation of the coupled governing equations for analysis in time and frequency domain. The weak form of the electromechanical/circuit system uses velocities and potential rate within the piezoelectric structure, free boundary charge on the electrodes, and potential at the level of the generic electric circuit as global degrees of freedom. The approximation of stress and dielectric displacement follows the work by Pian, Sze, and Pan. Results obtained with the proposed model are compared with analytical results for the reduced-order model of a cantilevered bimorph harvester with tip mass reported in the literature. The flexibility of the method is demonstrated by studying the influence of partial electrode coverage on the generated power output. [less ▲]

Towards a European health research and innovation cloud (HRIC)

in Genome Medicine (2020)

Towards a high-resolution drone-based 3D mapping dataset to optimise flood hazard modelling

in International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences (2019, June), XLII-2/W13

The occurrence of urban flooding following strong rainfall events may increase as a result of climate change. Urban expansion, ageing infrastructure and an increasing number of impervious surfaces are ... [more ▼]

The occurrence of urban flooding following strong rainfall events may increase as a result of climate change. Urban expansion, ageing infrastructure and an increasing number of impervious surfaces are further exacerbating flooding. To increase resilience and support flood mitigation, bespoke accurate flood modelling and reliable prediction is required. However, flooding in urban areas is most challenging. State-of-the-art flood inundation modelling is still often based on relatively low-resolution 2.5 D bare earth models with 2-5m GSD. Current systems suffer from a lack of precise input data and numerical instabilities and lack of other important data, such as drainage networks. Especially, the quality and resolution of the topographic input data represents a major source of uncertainty in urban flood modelling. A benchmark study is needed that defines the accuracy requirements for highly detailed urban flood modelling and to improve our understanding of important threshold processes and limitations of current methods and 3D mapping data alike. This paper presents the first steps in establishing a new, innovative multiscale data set suitable to benchmark urban flood modelling. The final data set will consist of high-resolution 3D mapping data acquired from different airborne platforms, focusing on the use of drones (optical and LiDAR). The case study includes residential as well as rural areas in Dudelange/Luxembourg, which have been prone to localized flash flooding following strong rainfall events in recent years. The project also represents a cross-disciplinary collaboration between the geospatial and flood modelling community. In this paper, we introduce the first steps to build up a new benchmark data set together with some initial flood modelling results. More detailed investigations will follow in the next phases of this project. [less ▲]