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ORBi

Lifetime prediction for solder joints with the extended finite element method ; ; et al in Proceedings of 12th Int. Conf. on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2011 (2011) Predicting the lifetime of solder joints undergoing thermal cycling is crucial for the electronics industry in order to guarantee a certain performance of their products in the field. Semi-empirical ... [more ▼] Predicting the lifetime of solder joints undergoing thermal cycling is crucial for the electronics industry in order to guarantee a certain performance of their products in the field. Semi-empirical methods are often used to predict the average lifetime of the critical joints. However, to get a reliable failure probability the standard deviation must also be addressed. The deviation of the lifetime from the mean value is a consequence of the variation in microstructure found in actual joints. We therefore propose a new methodology that calculates crack growth based on microstructural features of the joint. A series of random microstructures is generated. Crack growth calculations are performed for each of these structures. The structural problem is solved numerically with the extended finite element method which allows a complete automation of the process. The mean crack length and standard deviation are calculated from the crack growth simulations and the result is compared to experimental data. [less ▲] Detailed reference viewed: 108 (1 UL)A Lightweight Universal Gripper with Low Activation Force for Aerial Grasping Kremer, Paul ; Rahimi Nohooji, Hamed ; Sanchez Lopez, Jose Luis et al E-print/Working paper (2022) Soft robotic grippers have numerous advantages that address challenges in dynamic aerial grasping. Typical multi-fingered soft grippers recently showcased for aerial grasping are highly dependent on the ... [more ▼] Soft robotic grippers have numerous advantages that address challenges in dynamic aerial grasping. Typical multi-fingered soft grippers recently showcased for aerial grasping are highly dependent on the direction of the target object for successful grasping. This study pushes the boundaries of dynamic aerial grasping by developing an omnidirectional system for autonomous aerial manipulation. In particular, the paper investigates the design, fabrication, and experimental verification of a novel, highly integrated, modular, sensor-rich, universal jamming gripper specifically designed for aerial applications. Leveraging recent developments in particle jamming and soft granular materials, the presented gripper produces a substantial holding force while being very lightweight, energy-efficient and only requiring a low activation force. We show that the holding force can be improved by up to 50% by adding an additive to the membrane’s silicone mixture. The experiments show that our lightweight gripper can develop up to 15N of holding force with an activation force as low as 2.5N, even without geometric interlocking. Finally, a pick and release task is performed under real-world conditions by mounting the gripper onto a multi-copter. The developed aerial grasping system features many useful properties, such as resilience and robustness to collisions and the inherent passive compliance which decouples the UAV from the environment. [less ▲] Detailed reference viewed: 32 (1 UL)LINEAR BUCKLING ANALYSIS OF CRACKED ISOTROPIC PLATES USING THE EXTENDED FINITE ELEMENT METHOD ; ; et al Scientific Conference (2010, March) The behaviour of plate structures under compressive loads has been of great concern for engineering applications, especially in aeronautical and aerospace structures in which the demanding design of ... [more ▼] The behaviour of plate structures under compressive loads has been of great concern for engineering applications, especially in aeronautical and aerospace structures in which the demanding design of weight critical applications usually leads to stability problems. In this paper, the linear buckling problem of cracked isotropic plates is studied using the extended finite element method (XFEM). The mixed interpolation technique of the well-established MITC4 quadrilateral finite element with 12 standard degrees of freedom per element is used. The critical buckling load and mode shapes of simply supported square plates are computed as a function of crack length. [less ▲] Detailed reference viewed: 240 (0 UL)Linear buckling analysis of cracked plates by SFEM and XFEM ; ; Bordas, Stéphane et al in Journal of Mechanics of Material and Structures (2011), 6(9-10), 1213-1238 In this paper, the linear buckling problem for isotropic plates is studied using a quadrilateral element with smoothed curvatures and the extended finite element method. First, the curvature at each point ... [more ▼] In this paper, the linear buckling problem for isotropic plates is studied using a quadrilateral element with smoothed curvatures and the extended finite element method. First, the curvature at each point is obtained by a nonlocal approximation via a smoothing function. This element is later coupled with partition of unity enrichment to simplify the simulation of cracks. The proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. The buckling coefficient and mode shapes of square and rectangular plates are computed as functions of crack length, crack location, and plate thickness. The effects of different boundary conditions are also studied. © 2011 by Mathematical Sciences Publishers. [less ▲] Detailed reference viewed: 222 (0 UL)Linear identification of nonlinear systems: A lifting technique based on the Koopman operator Mauroy, Alexandre ; Goncalves, Jorge in Proceedings of the 55th IEEE Conference on Decision and Control (2016, December) We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state ... [more ▼] We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear identification technique by recasting the problem in the infinite-dimensional space of observables. This technique can be described in two main steps. In the first step, similar to a component of the Extended Dynamic Mode Decomposition algorithm, the data are lifted to the infinite-dimensional space and used for linear identification of the Koopman operator. In the second step, the obtained Koopman operator is “projected back” to the finite-dimensional state space, and identified to the nonlinear vector field through a linear least squares problem. The proposed technique is efficient to recover (polynomial) vector fields of different classes of systems, including unstable, chaotic, and open systems. In addition, it is robust to noise, well-suited to model low sampling rate datasets, and able to infer network topology and dynamics. [less ▲] Detailed reference viewed: 170 (8 UL)A Linear Programming Approach to Parameter Fitting for the Master Equation ; Goncalves, Jorge in IEEE Transactions on Automatic Control (2009), 54(10), 2451-2455 This technical note proposes a new framework for the design of continuous time, finite state space Markov processes. In particular, we propose a paradigm for selecting an optimal matrix within a pre ... [more ▼] This technical note proposes a new framework for the design of continuous time, finite state space Markov processes. In particular, we propose a paradigm for selecting an optimal matrix within a pre-specified pencil of transition rate matrices. Given any transition rate matrix specifying the time-evolution of the Markov process, we propose a class of figures of merit that upper-bounds the long-term evolution of any statistical moment. We show that optimization with respect to the aforementioned class of cost functions is tractable via dualization and linear programming methods. In addition, we suggest how this approach can be used as a tool for the sub-optimal design of the master equation, with performance guarantees. Our results are applied to illustrative examples. [less ▲] Detailed reference viewed: 119 (1 UL)Linear smoothed extended finite element method ; ; et al E-print/Working paper (n.d.) The extended finite element method (XFEM) was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to ... [more ▼] The extended finite element method (XFEM) was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to be split by a discontinuity, strong or weak and hence requires the integration of discontinuous functions or functions with discontinuous derivatives over elementary volumes. Moreover, in the case of open surfaces and singularities, special, usually non-polynomial functions must also be integrated.A variety of approaches have been proposed to facilitate these special types of numerical integration, which have been shown to have a large impact on the accuracy and convergence of the numerical solution. The smoothed extended finite element method (SmXFEM) [1], for example, makes numerical integration elegant and simple by transforming volume integrals into surface integrals. However, it was reported in [1, 2] that the strain smoothing is inaccurate when non-polynomial functions are in the basis. This is due to the constant smoothing function used over the smoothing domains which destroys the effect of the singularity. In this paper, we investigate the benefits of a recently developed Linear smoothing procedure [3] which provides better approximation to higher order polynomial fields in the basis. Some benchmark problems in the context of linear elastic fracture mechanics (LEFM) are solved to compare the standard XFEM, the constant-smoothed XFEM (Sm-XFEM) and the linear-smoothed XFEM (LSm-XFEM). We observe that the convergence rates of all three methods are the same. The stress intensity factors (SIFs) computed through the proposed LSm-XFEM are however more accurate than that obtained through Sm-XFEM. To conclude, compared to the conventional XFEM, the same order of accuracy is achieved at a relatively low computational effort. [less ▲] Detailed reference viewed: 142 (3 UL)Linear smoothed extended finite element method for fatigue crack growth simulations ; ; et al in Engineering Fracture Mechanics (2018), 206 In this paper, the recently proposed linear smoothed extended finite element method (LSmXFEM) is employed to simulate the fatigue crack growth. Unlike the conventional extended finite element method, the ... [more ▼] In this paper, the recently proposed linear smoothed extended finite element method (LSmXFEM) is employed to simulate the fatigue crack growth. Unlike the conventional extended finite element method, the LSmXFEM does not require special numerical integration technique to integrate the terms in the stiffness matrix. The stress intensity factors (SIFs) are evaluated by using the domain form of the interaction integral technique. The fatigue crack growth rate is evaluated using the generalized Paris’ law in conjunction with the maximum hoop stress criterion. The robustness of the method is demonstrated with a few examples for which the results are available in the literature. Then, the fatigue crack growth from the numerical simulation is compared with the experimental investigations performed on CR5 grade cold formed steel. It is seen that the fatigue life and the crack path obtained from the proposed method is in close agreement with the experimental observation. [less ▲] Detailed reference viewed: 88 (0 UL)A linear smoothed higher-order CS-FEM for the analysis of notched laminated composites ; ; et al in Engineering Analysis with Boundary Elements (2017), 85 Higher-order elements with highly accurate solutions are attractive for stress analysis and stress concentration problems. However, the distorted eight-node serendipity quadrilateral element is known to ... [more ▼] Higher-order elements with highly accurate solutions are attractive for stress analysis and stress concentration problems. However, the distorted eight-node serendipity quadrilateral element is known to yield inaccurate re- sults and sub-optimal convergence rate. In this paper, we present a higher order CS-FEM to alleviate the effect of distorted mesh and guarantee the quality of solutions by employing a linear smoothing technique over eight-node quadratic serendipity elements. The modified. strain matrix is computed by the divergence theorem between the nodal shape functions and their derivatives using Taylor’s expansion of the weak form. The proposed method eliminates the need for isoparametric mapping and numerical studies demonstrate that the proposed method is insensitive to mesh distortion. The improved accuracy and superior convergence rates are numerically demon- strated with a few benchmark problems. The analysis of the stress concentration around cutouts also proves that the present method has good performance for the laminated composites. [less ▲] Detailed reference viewed: 139 (1 UL)Linear smoothed polygonal and polyhedral finite elements ; ; Bordas, Stéphane et al E-print/Working paper (n.d.) It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal ... [more ▼] It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes to deliver improved accuracy and pass the patch test to machine precision. [less ▲] Detailed reference viewed: 471 (10 UL)A linear smoothed quadratic finite element for the analysis of laminated composite Reissner–Mindlin plates ; ; et al in Composite Structures (2017), 180 It is well known that the high-order elements have significantly improved the accuracy of solutions in the traditional finite element analysis, but the performance of high-order elements is restricted by ... [more ▼] It is well known that the high-order elements have significantly improved the accuracy of solutions in the traditional finite element analysis, but the performance of high-order elements is restricted by the shear-locking and distorted meshes for the plate problems. In this paper, a linear smoothed eight-node Reissner-Mindlin plate element (Q8 plate element) based on the first order shear deformation theory is developed for the static and free vibration analysis of laminated composite plates, the computation of the interior derivatives of shape function and isoparametric mapping can be removed. The strain matrices are modified with a linear smoothing technique by using the divergence theorem between the nodal shape functions and their derivatives in Taylor’s expansion. Moreover, the first order Taylor’s expansion is also employed for the construction of stiffness matrix to satisfy the linear strain distribution. Several numerical examples indicate that the novel Q8 plate element has good performance to alleviate the shear-locking phenomenon and improve the quality of the solutions with distorted meshes. [less ▲] Detailed reference viewed: 145 (2 UL)Linear smoothing over arbitrary polytopes ; ; et al Scientific Conference (n.d.) The conventional constant strain smoothing technique yields less accurate solutions that other techniques such as the conventional polygonal finite element method [1, 2]. In this work, we propose a linear ... [more ▼] The conventional constant strain smoothing technique yields less accurate solutions that other techniques such as the conventional polygonal finite element method [1, 2]. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex poly- topes. The method relies on sub-division of the polytope into simplical subcells; however instead of using a constant smoothing function, we employ a linear smoothing function over each subcell. This gives a new definition for the strain to compute the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the optimal convergence rate as in traditional quadrilateral and hexahedral finite elements. The accuracy is also improved, and all the methods tested pass the patch test to machine precision. [less ▲] Detailed reference viewed: 145 (0 UL)Linear smoothing over arbitrary polytopes for compressible and nearly incompressible linear elasticity ; Tomar, Satyendra ; Bordas, Stéphane et al Scientific Conference (2016, June) We present a displacement based approach over arbitrary polytopes for compressible and nearly incompressible linear elastic solids. In this approach, a volume-averaged nodal projection operator is ... [more ▼] We present a displacement based approach over arbitrary polytopes for compressible and nearly incompressible linear elastic solids. In this approach, a volume-averaged nodal projection operator is constructed to project the dilatational strain into an approximation space of equal or lower-order than the approximation space for the displacement field, resulting in a locking-free method. The formulation uses the usual Wachspress interpolants over arbitrary polytopes and the stability of the method is ensured by the addition of bubble like functions. The smoothed strains are evaluated based on the linear smoothing procedure. This further softens the bilinear form allowing the procedure to search for a solution satisfying the divergence- free condition. The divergence-free condition of the proposed approach is verified through systematic numerical study. The formulation delivers optimal convergence rates in the energy and L2-norms. Inf-sup tests are presented to demonstrated the stability of the formulation. [less ▲] Detailed reference viewed: 246 (3 UL)Link Optimization in Future Generation Satellite Systems Mengali, Alberto Doctoral thesis (2018) In recent years, communication networks have seen a huge growth in the amount of requested throughput, pushed from the combination of two main drivers: the introduction of new services and the improvement ... [more ▼] In recent years, communication networks have seen a huge growth in the amount of requested throughput, pushed from the combination of two main drivers: the introduction of new services and the improvement of existing ones, requiring increased amount of traffic (e.g. higher quality of video content). These effects mandate the constant evolution of current systems in order to cope with the growing user demand and should be tackled from multiple angles. On the one hand, better utilization of available resources might help in the short term to keep up with the market and has always been an important priority for operators of terrestrial and satellite networks alike. On the other hand, acquisition and exploitation of currently unused resources might fuel the growth for a significantly longer period of time, ensuring longevity and thus enabling future-proofing of current systems. Both these topics are addressed in this thesis with specific applications relevant to satellite communication networks. In the first part, this thesis focuses on maximization of the user capacity by better exploiting the available radio resources. Motivated by the substantial capacity gains enabled by a higher bandwidth allocation, we investigate the optimization of satellite systems employing full-frequency reuse on the user downlink. Unlike most of the literature on the subject, usually resorting to precoding techniques to mitigate the interference, we propose a combination of predistortion and precoding to jointly counteract on-board non-linear distortions and multi-user interference. First, a flexible framework for the optimization of transmit processing schemes in communication chains is presented. This framework expands on the application of the well known gradient descent technique by applying it to the maximization of the received Signal to Noise plus Interference ratio in complex communication systems. To do so, it identifies a suitable mathematical representation of various key blocks of the system and exploits the chain rule of the derivative to compute the overall gradient as a cascade of the single components. Afterwards, this framework is validated by optimizating the coefficients of the proposed predistortion architecture for the satellite system in analysis. The obtained results highlight the flexibility of the developed optimization framework and the benefits of the suggested predistortion strategy compared to existing state of the art solutions. In the second part of the thesis, the focus is shifted towards investigating the exploitation of novel resources by looking at the use of optical frequencies for ground-to-space feeder links. The topic is introduced by a survey of existing benefits and limitations of free space optical communications. Subsequently, the implications of employing optical frequencies in long distance ground-to-space feeder links with transparent satellites are addressed. Furthermore, a powerful and flexible simulation tool was developed and exploited during the course of this thesis to model and assess the Physical (PHY) layer performance of hybrid optical/Radio Frequencies (RF) satellite networks. This tool is presented together with the scenarios and results obtained as part of the project ONSET (Optical Feeder Links Study for Satellite Networks - ESA Contract No. 40000113462/15/NL/NDe). Finally, the thesis investigates a scenario that combines the transmit processing techniques analyzed in the first part and the context of optical feeder links evaluated in the second part. A hybrid optical/RF system is considered with an electrical predistorter in place to counteract the impairments induced by the combined effects of electrical and optical non-linearities encountered along the end-to-end chain. The developed mathematical framework is exploited to jointly optimize the predistortion coefficients and the working point for the electro-optical modulator. The performance results obtained after the optimization procedure demonstrate the efficacy of the proposed approach for hybrid optical/RF systems with analog modulations. [less ▲] Detailed reference viewed: 242 (34 UL)Linking Theories and Methods in Cognitive Sciences via Joint Embedding of the Scientific Literature: The Example of Cognitive Control Ansarinia, Morteza ; ; Cardoso-Leite, Pedro E-print/Working paper (2022) Traditionally, theory and practice of Cognitive Control are linked via literature reviews by human domain experts. This approach, however, is inadequate to track the ever-growing literature. It may also ... [more ▼] Traditionally, theory and practice of Cognitive Control are linked via literature reviews by human domain experts. This approach, however, is inadequate to track the ever-growing literature. It may also be biased, and yield redundancies and confusion. Here we present an alternative approach. We performed automated text analyses on a large body of scientific texts to create a joint representation of tasks and constructs. More specifically, 385,705 scientific abstracts were first mapped into an embedding space using a transformers-based language model. Document embeddings were then used to identify a task-construct graph embedding that grounds constructs on tasks and supports nuanced meaning of the constructs by taking advantage of constrained random walks in the graph. This joint task-construct graph embedding, can be queried to generate task batteries targeting specific constructs, may reveal knowledge gaps in the literature, and inspire new tasks and novel hypotheses. [less ▲] Detailed reference viewed: 41 (0 UL)A local dynamic route and green time swapping control algorithm maximizing total network capacity Viti, Francesco ; Rinaldi, Marco in Proceedings of the 25th Mediterranean Conference on Control and Automation, MED 2017 (2017) This paper deals with the traffic signal control problem. More specifically it investigates the impact at a network level of simple dynamic local traffic control policies. A dynamic route swapping rule is ... [more ▼] This paper deals with the traffic signal control problem. More specifically it investigates the impact at a network level of simple dynamic local traffic control policies. A dynamic route swapping rule is adopted to model the behavioral response of the travellers to signal changes, while a dynamic signal control swapping rule based on an equi-pressure policy is used to implicitly consider the flow response within the control updating process. Results on a simple network show that the flow responsive control policy outperforms pre-timed control, as well as a more conventional local control policy based on signal equi-saturation. Numerical results show also that the swapping rule based on equi-pressure is less susceptible to local optima, to systematically improve total network throughput, and to increase its effectiveness with when demand increases. © 2017 IEEE. [less ▲] Detailed reference viewed: 109 (1 UL)Local Nusselt number enhancements in liquid-liquid Taylor flows Mac Giolla Eain, Marc in International Journal of Heat and Mass Transfer (2015), 80 Detailed reference viewed: 103 (3 UL)Local vs. Global Search Strategies in Evolutionary GRID-based Conformational Sampling & Docking ; ; et al in 2009 IEEE CONGRESS ON EVOLUTIONARY COMPUTATION, VOLS 1-5 (2009) Conformational sampling, the computational prediction of the experimental geometries of small proteins (folding) or of protein-ligand complexes (docking), is often cited as one of the most challenging ... [more ▼] Conformational sampling, the computational prediction of the experimental geometries of small proteins (folding) or of protein-ligand complexes (docking), is often cited as one of the most challenging multimodal optimization problems. Due to the extreme ruggedness of the energy landscape as a function of geometry, sampling heuristics must rely on an appropriate trade-off between global and local searching efforts. A previously reported "planetary strategy", a generalization of the classical island model used to deploy a hybrid genetic algorithm on computer grids, has shown a good ability to quickly discover low-energy geometries of small proteins and sugars, and sometimes even pinpoint their native structures - although not reproducibly. The procedure focused on broad exploration and used a tabu strategy to avoid revisiting the neighborhood of known solutions, at the risk of "burying" important minima in overhastily set tabu areas. The strategy reported here, termed "divide-and-conquer planetary model" couples this global search procedure to a local search tool. Grid nodes are now shared between global and local exploration tasks. The phase space is cut into "cells" corresponding to a specified sampling width for each of the N degrees of freedom. Global search locates cells containing low-energy geometries. Local searches pinpoint even deeper minima within a cell. Sampling width controls the important trade-off between the number of cells and the local search effort needed to reproducibly sample each cell. The probability to submit a cell to local search depends on the energy of the most stable geometry found within. Local searches are allotted limited resources and are not expected to converge. However, as long as they manage to discover some deeper local minima, the explored cell remains eligible for further local search, now relying on the improved energy level to enhance chances to be picked again. This competition prevents the system to waste too much effort in fruitless local searches. Eventually, after a limited number of local searches, a cell will be "closed" and used - first as "seed", later as tabu zone - to bias future global searches. Technical details and some folding and docking results will be discussed. [less ▲] Detailed reference viewed: 63 (0 UL)Local/global model order reduction strategy for the simulation of quasi-brittle fracture ; ; Bordas, Stéphane in International Journal for Numerical Methods in Engineering (2012), 89(2), 154-179 This paper proposes a novel technique to reduce the computational burden associated with the simulation of localized failure. The proposed methodology affords the simulation of damage initiation and ... [more ▼] This paper proposes a novel technique to reduce the computational burden associated with the simulation of localized failure. The proposed methodology affords the simulation of damage initiation and propagation while concentrating the computational effort where it is most needed, that is, in the localization zones. To do so, a local/global technique is devised where the global (slave) problem (far from the zones undergoing severe damage and cracking) is solved for in a reduced space computed by the classical proper orthogonal decomposition while the local (master) degrees of freedom (associated with the part of the structure where most of the damage is taking place) are fully resolved. Both domains are coupled through a local/global technique. This method circumvents the difficulties associated with model order reduction for the simulation of highly nonlinear mechanical failure and offers an alternative or complementary approach to the development of multiscale fracture simulators. © 2011 John Wiley & Sons, Ltd. [less ▲] Detailed reference viewed: 266 (7 UL)Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions ; Bourantas, Georgios ; in Computational Mechanics (2011), 47(2), 137-159 In this article a numerical solution of the time dependent, coupled system equations of magnetohydrody- namics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method ... [more ▼] In this article a numerical solution of the time dependent, coupled system equations of magnetohydrody- namics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method. The approxima- tion of the field variables is obtained with the moving least squares (MLS) approximation. Regular and irregular nodal distributions are used. Thus, a numerical solver is developed for the unsteady coupled MHD problems, using the collo- cation formulation, for regular and irregular cross sections, as are the rectangular, triangular and circular. Arbitrary wall conductivity conditions are applied when a uniform mag- netic field is imposed at characteristic directions relative to the flow one. Velocity and induced magnetic field across the section have been evaluated at various time intervals for sev- eral Hartmann numbers (up to 105) and wall conductivities. The numerical results of the strong-form MPC method are compared with those obtained using two weak-form mesh- less methods, that is, the local boundary integral equation (LBIE) meshless method and the meshless local Petrov– Galerkin (MLPG) method, and with the analytical solutions, where they are available. Furthermore, the accuracy of the method is assessed in terms of the error norms L 2 and L ∞ , the number of nodes in the domain of influence and the time step length depicting the convergence rate of the method. Run time results are also presented demonstrating the efficiency and the applicability of the method for real world problems. [less ▲] Detailed reference viewed: 126 (1 UL) |
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