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Results on meshless collocation techniques

Leevan Ling, Roland Opfer, Robert Schaback
2006 Engineering analysis with boundary elements  
Furthermore, a greedy variation of this technique is provided, allowing a fully adaptive matrix-free and data-dependent meshless selection of the test and trial spaces.  ...  Kansa [7, 8] is very successful in engineering applications, there were no proven results so far on the unsymmetric meshless collocation method for solving PDE boundary value problems in strong form.  ...  Conclusion We propose a truly meshless adaptive greedy technique that allows general PDE problems to be solved on complicated domains.  ... 
doi:10.1016/j.enganabound.2005.08.008 fatcat:hhdvmrubvrbcxmx26osiesw7km

Identification of Crack Profiles using Database and Greedy Search Inverse Analysis Arising in Eddy Current Testing

Thanh-Duong Nguyen, Fumio Kojima
2010 Transactions of the Institute of Systems Control and Information Engineers  
This inversion technique uses Greedy search algorithm to find the optimum of least-square error between measurement signals and simulation data.  ...  This paper is concerned with an optimization method to recover crack profiles from measurement signals obtained by eddy current testing.  ...  Greedy algorithms find the overall, or globally, optimal solution for some optimization problems, but may find lessthan-optimal solutions for some instances of other problems, especially when the problem  ... 
doi:10.5687/iscie.23.74 fatcat:swblhrlaybegdkpdsoy7x7o5nu

Rapid inverse parameter estimation using reduced-basis approximation with asymptotic error estimation

G.R. Liu, Khin Zaw, Y.Y. Wang
2008 Computer Methods in Applied Mechanics and Engineering  
This paper presents a rapid and reliable approach to solve inverse problems of parameter estimation for structural systems using reduced-basis method (RBM).  ...  A genetic algorithm (GA) is then used in the inverse search procedure for parameter estimation.  ...  Huynh (Singapore-MIT Alliance) for his suggestions and the discussions during the course of this work.  ... 
doi:10.1016/j.cma.2008.03.012 fatcat:h7dqkgri5fdvjiotpynks5tiom

A method of fast, sequential experimental design for linearized geophysical inverse problems

Darrell A. Coles, Frank Dale Morgan
2009 Geophysical Journal International  
The issue of design for inherently ill-posed inverse problems is considered and an approach for circumventing such problems is proposed.  ...  S U M M A R Y An algorithm for linear(ized) experimental design is developed for a determinant-based design objective function.  ...  Sequential Another way to get around the problem of determinant-based survey designs for ill-posed inverse problems is to design with respect to the regularized inverse problem.  ... 
doi:10.1111/j.1365-246x.2009.04156.x fatcat:53bkpa4khfacpdnbxtellh2krq

An improved subspace selection algorithm for meshless collocation methods

Leevan Ling, Robert Schaback
2009 International Journal for Numerical Methods in Engineering  
Choosing data points is a common problem for researchers who employ various meshless methods for solving partial differential equations.  ...  Such complexity makes the hope of having an optimal centers placement unpromising.  ...  Hence, for problems with incompatible boundary conditions, new-Greedy with a large c can be seen as an efficient approach to obtain a smooth approximation.  ... 
doi:10.1002/nme.2674 fatcat:vqvoepqol5e4xczjlvmbxq25ke

Stable and Convergent Unsymmetric Meshless Collocation Methods

Leevan Ling, Robert Schaback
2008 SIAM Journal on Numerical Analysis  
This means that (except for the startup phase, which is postponed here) we always keep the inverse C of a (m + 2) x (ra + 2) matrix The revised simplex method based on (6.1) already is an on-the-fly technique  ...  In particular, we combine an adaptive greedy method with linear programming, and some numerical examples show that our new adaptive on-the-fly algorithm works stably in spite of large condition numbers  ... 
doi:10.1137/06067300x fatcat:hn3rbodylvhlbbb2axhupghcb4

Interactive Deformations with Multigrid Skeletal Constraints [article]

Joachim Georgii, Daniel Lagler, Christian Dick, Rüdiger Westermann
2010 Workshop on Virtual Reality Interactions and Physical Simulations  
In this paper we present an interactive method for simulating deformable objects using skeletal constraints.  ...  The skeleton pose is determined via inverse kinematics. The target positions of joints are either given by user interactions or forces imposed by the surrounding deformable body.  ...  By using an inverse kinematic approach, we can update the pose of the skeleton, which then determines the boundary conditions in the finite element simulation.  ... 
doi:10.2312/pe/vriphys/vriphys10/039-047 dblp:conf/vriphys/GeorgiiLDW10 fatcat:szfn6gyyorc33htbaadqxv2wgq

Inline hologram reconstruction with sparsity constraints

Loïc Denis, Dirk Lorenz, Eric Thiébaut, Corinne Fournier, Dennis Trede
2009 Optics Letters  
Classical linear reconstructions yield images with artifacts such as distortions near the field-of-view boundaries or twin-images.  ...  Additional processing, such as maximum-of-focus detection, is thus unavoidable for any successful use of the reconstructed volume.  ...  Refregier for fruitful discussions, and to C. Mennessier and D. Ghosh Roy for their careful reading of the manuscript.  ... 
doi:10.1364/ol.34.003475 pmid:19927182 fatcat:dl3axifinnhmnkqaxc7akqxaua

Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space

T. Bui-Thanh, K. Willcox, O. Ghattas
2008 SIAM Journal on Scientific Computing  
We pose the task of determining appropriate sample points as a PDE-constrained optimization problem, which is implemented using an efficient adaptive algorithm that scales well to systems with a large  ...  A model-constrained adaptive sampling methodology is proposed for reduction of large-scale systems with high-dimensional parametric input spaces.  ...  In [14, 15] , the greedy sampling algorithm was combined with an a posteriori error estimator and applied to optimal control and inverse problems.  ... 
doi:10.1137/070694855 fatcat:2qbhphnac5enfaetqyitzfvjfq

Hessian-based model reduction for large-scale systems with initial-condition inputs

O. Bashir, K. Willcox, O. Ghattas, B. van Bloemen Waanders, J. Hill
2008 International Journal for Numerical Methods in Engineering  
We consider the problem of determining a reduced model of an initial value problem that spans all important initial conditions, and pose the task of determining appropriate training sets for reduced-basis  ...  optimal design, optimal control, and inverse problem applications.  ...  The approach is motivated by the greedy algorithm of [20] , which proposed an adaptive approach to determine the parameter locations at which samples are drawn to form a reduced basis.  ... 
doi:10.1002/nme.2100 fatcat:vof5a5mjtjfctibhdh3zpqy62y

Minimum sized text containment shapes

Nathan Hurst, Kim Marriott, Peter Moulder
2006 Proceedings of the 2006 ACM symposium on Document engineering - DocEng '06  
We use a variant of secant search to determine the minimum area for the shape, guided by the area of the text.  ...  A variant of this problem is to take a fixed shape and determine the maximal size font that will still allow the content to fit into it.  ...  Acknowledgements We'd like to Thank Jonathan Wright for his help and the members of the Adaptive Diagrams Research Group for their interest and suggestions.  ... 
doi:10.1145/1166160.1166165 dblp:conf/doceng/HurstMM06 fatcat:opwx3de6prdobgyhkuofqesgky

Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage

Nanda Kishore Bellam Muralidhar, Natalie Rauter, Andrey Mikhaylenko, Rolf Lammering, Dirk A. Lorenz
2021 Modelling  
An adaptive parameter sampling technique is established with the aid of a surrogate model to efficiently update the reduced-order basis in a greedy fashion.  ...  This can be achieved by the inverse problem analysis approach, which employs the signal measurement data recorded by the embedded sensors in the structure.  ...  Acknowledgments: The authors wish to thank the anonymous reviewers for their valuable comments and helpful suggestions, which greatly improved and clarified this paper.  ... 
doi:10.3390/modelling2040031 fatcat:iq6mbp3p2vdwfcuy25mfn3jrw4

Page 1980 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
Mogin and Sonja Ristic, An algorithm for determination of pri- mary key candidates in the relational database schema (329-335); Zoran Ognjanovic and Uros Majstorovic, AND-parallel prolog for PC-based  ...  Acketa, A greedy optimal solution for digital con- vex polygons with minimal area (305-311); Miodrag J.  ... 

Alternatives for Generating a Reduced Basis to Solve the Hyperspectral Diffuse Optical Tomography Model [article]

Rachel Grotheer, Thilo Strauss, Phil Gralla, Taufiquar Khan
2018 arXiv   pre-print
For this one-dimensional problem, we find that both the Metropolis and gradient algorithms are potentially superior alternatives to the greedy algorithm in that they generate a reduced basis which produces  ...  The governing equation for hyDOT is an elliptic PDE parameterized by the wavelength of the laser source.  ...  Gralla was supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) for subproject C2 Oberflchenoptimierung within in the SFB 747 (Collaborative Research Center) Mikrokaltumformen  ... 
arXiv:1803.00948v1 fatcat:ztdmxhyflnhjbc5mpzgd3rajea

Adaptive Reduced Basis Methods for Nonlinear Convection–Diffusion Equations [chapter]

Martin Drohmann, Bernard Haasdonk, Mario Ohlberger
2011 Springer Proceedings in Mathematics  
The latter is usually realized by an adaptive search for base functions in the parameter space.  ...  The complexity of the problem setting requires the use of several new techniques like parametrized empirical operator interpolation, efficient a posteriori error estimation and adaptive generation of reduced  ...  Such scenarios might occur in parameter studies, optimization, control, inverse problems or statistical analysis for a given parametrized problem.  ... 
doi:10.1007/978-3-642-20671-9_39 fatcat:36teqzhk3ra6zp45aomj63bq7e
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