Chen, C. S.; Noorizadegan, Amir; Young, D. L.; Chen, Chuin-Shan On the determination of locating the source points of the MFS using effective condition number. (English) Zbl 1505.65307 J. Comput. Appl. Math. 423, Article ID 114955, 15 p. (2023). MSC: 65N80 65N85 65F35 65F20 65N20 65N15 35J05 31A30 PDFBibTeX XMLCite \textit{C. S. Chen} et al., J. Comput. Appl. Math. 423, Article ID 114955, 15 p. (2023; Zbl 1505.65307) Full Text: DOI
Brubeck, Pablo D.; Trefethen, Lloyd N. Lightning Stokes solver. (English) Zbl 1509.41008 SIAM J. Sci. Comput. 44, No. 3, A1205-A1226 (2022). Reviewer: Francisco Pérez Acosta (La Laguna) MSC: 41A20 65N35 76D07 PDFBibTeX XMLCite \textit{P. D. Brubeck} and \textit{L. N. Trefethen}, SIAM J. Sci. Comput. 44, No. 3, A1205--A1226 (2022; Zbl 1509.41008) Full Text: DOI arXiv
Chang, Jen-Yi; Chen, Ru-Yun; Tsai, Chia-Cheng A comparative study on polynomial expansion method and polynomial method of particular solutions. (English) Zbl 1499.35167 Adv. Appl. Math. Mech. 14, No. 3, 577-595 (2022). MSC: 35C11 65N35 PDFBibTeX XMLCite \textit{J.-Y. Chang} et al., Adv. Appl. Math. Mech. 14, No. 3, 577--595 (2022; Zbl 1499.35167) Full Text: DOI
Jiang, Quan; Zhou, Zhidong; Yang, Fengpeng A new approach to solve the anti-plane crack problems by the method of fundamental solutions. (English) Zbl 1521.74193 Eng. Anal. Bound. Elem. 135, 284-298 (2022). MSC: 74R10 65N80 74S99 PDFBibTeX XMLCite \textit{Q. Jiang} et al., Eng. Anal. Bound. Elem. 135, 284--298 (2022; Zbl 1521.74193) Full Text: DOI
da Silva, W. B.; Dutra, J. C. S.; Kopperschimidt, C. E. P.; Lesnic, D.; Aykroyd, R. G. Sequential estimation of the time-dependent heat transfer coefficient using the method of fundamental solutions and particle filters. (English) Zbl 07484759 Inverse Probl. Sci. Eng. 29, No. 13, 3322-3341 (2021). MSC: 62L12 65M12 PDFBibTeX XMLCite \textit{W. B. da Silva} et al., Inverse Probl. Sci. Eng. 29, No. 13, 3322--3341 (2021; Zbl 07484759) Full Text: DOI
Reddy, G. M. M.; Nanda, P.; Vynnycky, M.; Cuminato, J. A. An adaptive boundary algorithm for the reconstruction of boundary and initial data using the method of fundamental solutions for the inverse Cauchy-Stefan problem. (English) Zbl 1476.65274 Comput. Appl. Math. 40, No. 3, Paper No. 99, 26 p. (2021). MSC: 65M80 65M30 65M32 PDFBibTeX XMLCite \textit{G. M. M. Reddy} et al., Comput. Appl. Math. 40, No. 3, Paper No. 99, 26 p. (2021; Zbl 1476.65274) Full Text: DOI
Wang, Fajie; Zhao, Qinghai; Chen, Zengtao; Fan, Chia-Ming Localized Chebyshev collocation method for solving elliptic partial differential equations in arbitrary 2D domains. (English) Zbl 1508.65166 Appl. Math. Comput. 397, Article ID 125903, 14 p. (2021). MSC: 65N35 35J05 PDFBibTeX XMLCite \textit{F. Wang} et al., Appl. Math. Comput. 397, Article ID 125903, 14 p. (2021; Zbl 1508.65166) Full Text: DOI
Jiang, Quan; Zhou, Zhidong; Chen, Jubing; Yang, Fengpeng The method of fundamental solutions for two-dimensional elasticity problems based on the Airy stress function. (English) Zbl 1521.74419 Eng. Anal. Bound. Elem. 130, 220-237 (2021). MSC: 74S99 65N80 74B05 PDFBibTeX XMLCite \textit{Q. Jiang} et al., Eng. Anal. Bound. Elem. 130, 220--237 (2021; Zbl 1521.74419) Full Text: DOI
Chen, C. S.; Amuzu, Lionel; Acheampong, Kwesi; Zhu, Huiqing Improved geometric modeling using the method of fundamental solutions. (English) Zbl 1521.65135 Eng. Anal. Bound. Elem. 130, 49-57 (2021). MSC: 65N80 65D18 PDFBibTeX XMLCite \textit{C. S. Chen} et al., Eng. Anal. Bound. Elem. 130, 49--57 (2021; Zbl 1521.65135) Full Text: DOI
Young, D. L.; Lin, Shin-Ruei; Chen, Chuin-Shan; Chen, C. S. Two-step MPS-MFS ghost point method for solving partial differential equations. (English) Zbl 1524.65901 Comput. Math. Appl. 94, 38-46 (2021). MSC: 65N35 65D05 35J05 35J25 65N38 65N80 65D17 65N85 PDFBibTeX XMLCite \textit{D. L. Young} et al., Comput. Math. Appl. 94, 38--46 (2021; Zbl 1524.65901) Full Text: DOI
Abbasbandy, Saeid; Shivanian, Elyas; AL-Jizani, Khalid Hammood; Atluri, Satya N. Pseudospectral meshless radial point interpolation for generalized biharmonic equation subject to simply supported and clamped boundary conditions. (English) Zbl 1464.65192 Eng. Anal. Bound. Elem. 125, 23-32 (2021). MSC: 65N35 35J15 65D12 PDFBibTeX XMLCite \textit{S. Abbasbandy} et al., Eng. Anal. Bound. Elem. 125, 23--32 (2021; Zbl 1464.65192) Full Text: DOI
Liu, Qingguo; Šarler, Božidar Method of fundamental solutions without fictitious boundary for anisotropic elasticity problems based on mechanical equilibrium desingularization. (English) Zbl 1453.65433 Alves, Carlos (ed.) et al., Advances in Trefftz methods and their applications. Selected papers based on the presentations at the 9th conference on Trefftz methods and 5th conference on method of fundamental solutions, Lisbon, Portugal, July 29–31, 2019. Cham: Springer. SEMA SIMAI Springer Ser. 23, 59-86 (2020). MSC: 65N80 65N35 74B05 74E10 74S99 35Q74 PDFBibTeX XMLCite \textit{Q. Liu} and \textit{B. Šarler}, SEMA SIMAI Springer Ser. 23, 59--86 (2020; Zbl 1453.65433) Full Text: DOI
Cheng, Alexander H. D.; Hong, Yongxing An overview of the method of fundamental solutions – solvability, uniqueness, convergence, and stability. (English) Zbl 1464.65264 Eng. Anal. Bound. Elem. 120, 118-152 (2020). MSC: 65N80 65N12 PDFBibTeX XMLCite \textit{A. H. D. Cheng} and \textit{Y. Hong}, Eng. Anal. Bound. Elem. 120, 118--152 (2020; Zbl 1464.65264) Full Text: DOI
Mierzwiczak, Magdalena; Kołodziej, Jan Adam Comparison of three meshless methods for 2D harmonic and biharmonic problems. (English) Zbl 1464.65212 Eng. Anal. Bound. Elem. 118, 157-168 (2020). MSC: 65N35 65N80 PDFBibTeX XMLCite \textit{M. Mierzwiczak} and \textit{J. A. Kołodziej}, Eng. Anal. Bound. Elem. 118, 157--168 (2020; Zbl 1464.65212) Full Text: DOI
Ye, Zhuan Regularity results for the 2D critical Oldroyd-B model in the corotational case. (English) Zbl 1440.76009 Proc. R. Soc. Edinb., Sect. A, Math. 150, No. 4, 1871-1913 (2020). MSC: 76A10 76D03 76A05 35Q35 PDFBibTeX XMLCite \textit{Z. Ye}, Proc. R. Soc. Edinb., Sect. A, Math. 150, No. 4, 1871--1913 (2020; Zbl 1440.76009) Full Text: DOI
Zhu, Xiaomin; Dou, Fangfang; Karageorghis, Andreas; Chen, C. S. A fictitious points one-step MPS-MFS technique. (English) Zbl 1508.65174 Appl. Math. Comput. 382, Article ID 125332, 15 p. (2020). MSC: 65N80 PDFBibTeX XMLCite \textit{X. Zhu} et al., Appl. Math. Comput. 382, Article ID 125332, 15 p. (2020; Zbl 1508.65174) Full Text: DOI
Shivanian, Elyas; Abbasbandy, Saeid Pseudospectral meshless radial point interpolation for generalized biharmonic equation in the presence of Cahn-Hilliard conditions. (English) Zbl 1449.65336 Comput. Appl. Math. 39, No. 3, Paper No. 148, 18 p. (2020). MSC: 65N35 65D05 31A30 PDFBibTeX XMLCite \textit{E. Shivanian} and \textit{S. Abbasbandy}, Comput. Appl. Math. 39, No. 3, Paper No. 148, 18 p. (2020; Zbl 1449.65336) Full Text: DOI
Liu, Chein-Shan; Qiu, Lin; Lin, Ji Simulating thin plate bending problems by a family of two-parameter homogenization functions. (English) Zbl 1481.74497 Appl. Math. Modelling 79, 284-299 (2020). MSC: 74K20 PDFBibTeX XMLCite \textit{C.-S. Liu} et al., Appl. Math. Modelling 79, 284--299 (2020; Zbl 1481.74497) Full Text: DOI
Wang, Fajie; Fan, Chia-Ming; Hua, Qingsong; Gu, Yan Localized MFS for the inverse Cauchy problems of two-dimensional Laplace and biharmonic equations. (English) Zbl 1433.65338 Appl. Math. Comput. 364, Article ID 124658, 14 p. (2020). MSC: 65N80 35R30 35J05 PDFBibTeX XMLCite \textit{F. Wang} et al., Appl. Math. Comput. 364, Article ID 124658, 14 p. (2020; Zbl 1433.65338) Full Text: DOI
Lin, Ji; Xu, Yi; Zhang, Yuhui Simulation of linear and nonlinear advection-diffusion-reaction problems by a novel localized scheme. (English) Zbl 1437.65211 Appl. Math. Lett. 99, Article ID 106005, 9 p. (2020). MSC: 65N35 35J25 PDFBibTeX XMLCite \textit{J. Lin} et al., Appl. Math. Lett. 99, Article ID 106005, 9 p. (2020; Zbl 1437.65211) Full Text: DOI
Arora, Surbhi; Dabas, Jaydev Inverse heat conduction problem in two-dimensional anisotropic medium. (English) Zbl 1459.35389 Int. J. Appl. Comput. Math. 5, No. 6, Paper No. 161, 24 p. (2019). MSC: 35R30 35A08 35K05 35R25 65M32 PDFBibTeX XMLCite \textit{S. Arora} and \textit{J. Dabas}, Int. J. Appl. Comput. Math. 5, No. 6, Paper No. 161, 24 p. (2019; Zbl 1459.35389) Full Text: DOI
Liu, Q. G.; Šarler, B. Method of fundamental solutions without fictitious boundary for three dimensional elasticity problems based on force-balance desingularization. (English) Zbl 1464.74402 Eng. Anal. Bound. Elem. 108, 244-253 (2019). MSC: 74S99 65N80 74B05 PDFBibTeX XMLCite \textit{Q. G. Liu} and \textit{B. Šarler}, Eng. Anal. Bound. Elem. 108, 244--253 (2019; Zbl 1464.74402) Full Text: DOI
Chang, Jen-Yi; Tsai, Chia-Cheng; Young, D. L. Homotopy method of fundamental solutions for solving nonlinear heat conduction problems. (English) Zbl 1464.80045 Eng. Anal. Bound. Elem. 108, 179-191 (2019). MSC: 80M99 65N80 80A19 PDFBibTeX XMLCite \textit{J.-Y. Chang} et al., Eng. Anal. Bound. Elem. 108, 179--191 (2019; Zbl 1464.80045) Full Text: DOI
Xie, Yaning; Ying, Wenjun; Wang, Wei-Cheng A high-order kernel-free boundary integral method for the biharmonic equation on irregular domains. (English) Zbl 1428.65103 J. Sci. Comput. 80, No. 3, 1681-1699 (2019). MSC: 65N38 31A30 65N06 65T50 PDFBibTeX XMLCite \textit{Y. Xie} et al., J. Sci. Comput. 80, No. 3, 1681--1699 (2019; Zbl 1428.65103) Full Text: DOI
Gáspár, Csaba A multi-level technique for the method of fundamental solutions without regularization and desingularization. (English) Zbl 1464.65268 Eng. Anal. Bound. Elem. 103, 145-159 (2019). MSC: 65N80 PDFBibTeX XMLCite \textit{C. Gáspár}, Eng. Anal. Bound. Elem. 103, 145--159 (2019; Zbl 1464.65268) Full Text: DOI
Piltner, Reinhard Some remarks on Trefftz type approximations. (English) Zbl 1464.74380 Eng. Anal. Bound. Elem. 101, 102-112 (2019). MSC: 74S70 65N35 PDFBibTeX XMLCite \textit{R. Piltner}, Eng. Anal. Bound. Elem. 101, 102--112 (2019; Zbl 1464.74380) Full Text: DOI
Dou, Fangfang; Li, Zi-Cai; Chen, C. S.; Tian, Zhaolu Analysis on the method of fundamental solutions for biharmonic equations. (English) Zbl 1429.65293 Appl. Math. Comput. 339, 346-366 (2018). MSC: 65N80 35J08 35J40 35J05 PDFBibTeX XMLCite \textit{F. Dou} et al., Appl. Math. Comput. 339, 346--366 (2018; Zbl 1429.65293) Full Text: DOI
Grabski, Jakub Krzysztof; Kołodziej, Jan Adam Laminar fluid flow and heat transfer in an internally corrugated tube by means of the method of fundamental solutions and radial basis functions. (English) Zbl 1409.65108 Comput. Math. Appl. 75, No. 4, 1413-1433 (2018). MSC: 65N80 65N35 PDFBibTeX XMLCite \textit{J. K. Grabski} and \textit{J. A. Kołodziej}, Comput. Math. Appl. 75, No. 4, 1413--1433 (2018; Zbl 1409.65108) Full Text: DOI
Liu, Q. G.; Šarler, Bozidar Non-singular method of fundamental solutions for elasticity problems in three-dimensions. (English) Zbl 1403.74313 Eng. Anal. Bound. Elem. 96, 23-35 (2018). MSC: 74S30 65N80 74B05 PDFBibTeX XMLCite \textit{Q. G. Liu} and \textit{B. Šarler}, Eng. Anal. Bound. Elem. 96, 23--35 (2018; Zbl 1403.74313) Full Text: DOI
Lin, Ji; Lamichhane, A. R.; Chen, C. S.; Lu, Jun The adaptive algorithm for the selection of sources of the method of fundamental solutions. (English) Zbl 1403.65257 Eng. Anal. Bound. Elem. 95, 154-159 (2018). MSC: 65N80 PDFBibTeX XMLCite \textit{J. Lin} et al., Eng. Anal. Bound. Elem. 95, 154--159 (2018; Zbl 1403.65257) Full Text: DOI
Trefethen, Lloyd N. Series solution of Laplace problems. (English) Zbl 1400.31001 ANZIAM J. 60, No. 1, 1-26 (2018). MSC: 31A05 35J05 35J08 31-01 35-01 PDFBibTeX XMLCite \textit{L. N. Trefethen}, ANZIAM J. 60, No. 1, 1--26 (2018; Zbl 1400.31001) Full Text: DOI arXiv
Yang, J. J.; Zheng, J. L.; Wen, P. H. Generalized method of fundamental solutions (GMFS) for boundary value problems. (English) Zbl 1403.65237 Eng. Anal. Bound. Elem. 94, 25-33 (2018). MSC: 65N38 35J05 65N80 PDFBibTeX XMLCite \textit{J. J. Yang} et al., Eng. Anal. Bound. Elem. 94, 25--33 (2018; Zbl 1403.65237) Full Text: DOI Link
Rostamian, Malihe; Shahrezaee, Alimardan A meshless method for solving 1D time-dependent heat source problem. (English) Zbl 1398.65281 Inverse Probl. Sci. Eng. 26, No. 1, 51-82 (2018). MSC: 65N21 35K05 35R30 PDFBibTeX XMLCite \textit{M. Rostamian} and \textit{A. Shahrezaee}, Inverse Probl. Sci. Eng. 26, No. 1, 51--82 (2018; Zbl 1398.65281) Full Text: DOI
Kpogan, Kékéli; Tri, Abdeljalil; Sogah, Amen; Mathieu, Norman; Zahrouni, Hamid; Potier-Ferry, Michel Combining MFS and PGD methods to solve transient heat equation. (English) Zbl 1383.65131 Numer. Methods Partial Differ. Equations 34, No. 1, 257-273 (2018). MSC: 65M80 35K05 PDFBibTeX XMLCite \textit{K. Kpogan} et al., Numer. Methods Partial Differ. Equations 34, No. 1, 257--273 (2018; Zbl 1383.65131) Full Text: DOI
Lin, Ji; Chen, C. S.; Wang, Fajie; Dangal, Thir Method of particular solutions using polynomial basis functions for the simulation of plate bending vibration problems. (English) Zbl 1480.74115 Appl. Math. Modelling 49, 452-469 (2017). MSC: 74H45 74K20 PDFBibTeX XMLCite \textit{J. Lin} et al., Appl. Math. Modelling 49, 452--469 (2017; Zbl 1480.74115) Full Text: DOI
Gu, Yan; Gao, Hongwei; Chen, Wen; Wang, Huijuan; Zhang, Chuanzeng A general algorithm for evaluating nearly strong-singular (and beyond) integrals in three-dimensional boundary element analysis. (English) Zbl 1398.65325 Comput. Mech. 59, No. 5, 779-793 (2017). MSC: 65N38 74S15 65D32 41A55 65R20 PDFBibTeX XMLCite \textit{Y. Gu} et al., Comput. Mech. 59, No. 5, 779--793 (2017; Zbl 1398.65325) Full Text: DOI
Marner, F.; Gaskell, P. H.; Scholle, M. A complex-valued first integral of Navier-Stokes equations: unsteady Couette flow in a corrugated channel system. (English) Zbl 1360.76079 J. Math. Phys. 58, No. 4, 043102, 19 p. (2017). MSC: 76D05 35Q30 PDFBibTeX XMLCite \textit{F. Marner} et al., J. Math. Phys. 58, No. 4, 043102, 19 p. (2017; Zbl 1360.76079) Full Text: DOI Link
Liu, Q. G.; Šarler, Bozidar Improved non-singular method of fundamental solutions for two-dimensional isotropic elasticity problems with elastic/rigid inclusions or voids. (English) Zbl 1403.74311 Eng. Anal. Bound. Elem. 68, 24-34 (2016). MSC: 74S30 65N80 74B05 PDFBibTeX XMLCite \textit{Q. G. Liu} and \textit{B. Šarler}, Eng. Anal. Bound. Elem. 68, 24--34 (2016; Zbl 1403.74311) Full Text: DOI
Amirfakhrian, M.; Arghand, M.; Kansa, E. J. A new approximate method for an inverse time-dependent heat source problem using fundamental solutions and RBFs. (English) Zbl 1403.65051 Eng. Anal. Bound. Elem. 64, 278-289 (2016). MSC: 65M32 PDFBibTeX XMLCite \textit{M. Amirfakhrian} et al., Eng. Anal. Bound. Elem. 64, 278--289 (2016; Zbl 1403.65051) Full Text: DOI
Lockerby, D. A.; Collyer, B. Fundamental solutions to moment equations for the simulation of microscale gas flows. (English) Zbl 1383.76399 J. Fluid Mech. 806, 413-436 (2016). MSC: 76N15 PDFBibTeX XMLCite \textit{D. A. Lockerby} and \textit{B. Collyer}, J. Fluid Mech. 806, 413--436 (2016; Zbl 1383.76399) Full Text: DOI
Gu, Yan; Chen, Wen; Gao, Hongwei; Zhang, Chuanzeng A meshless singular boundary method for three-dimensional elasticity problems. (English) Zbl 1352.74039 Int. J. Numer. Methods Eng. 107, No. 2, 109-126 (2016). MSC: 74B05 74S15 65N38 PDFBibTeX XMLCite \textit{Y. Gu} et al., Int. J. Numer. Methods Eng. 107, No. 2, 109--126 (2016; Zbl 1352.74039) Full Text: DOI
Chen, C. S.; Karageorghis, Andreas; Li, Yan On choosing the location of the sources in the MFS. (English) Zbl 1338.65269 Numer. Algorithms 72, No. 1, 107-130 (2016). MSC: 65N80 35J05 35J30 PDFBibTeX XMLCite \textit{C. S. Chen} et al., Numer. Algorithms 72, No. 1, 107--130 (2016; Zbl 1338.65269) Full Text: DOI
Fam, George S. A.; Rashed, Youssef F. An efficient meshless technique for the solution of transversely isotropic two-dimensional piezoelectricity. (English) Zbl 1443.65428 Comput. Math. Appl. 69, No. 5, 438-454 (2015). MSC: 65N80 74F15 78M99 PDFBibTeX XMLCite \textit{G. S. A. Fam} and \textit{Y. F. Rashed}, Comput. Math. Appl. 69, No. 5, 438--454 (2015; Zbl 1443.65428) Full Text: DOI
Kołodziej, Jan Adam; Grabski, Jakub Krzysztof Application of the method of fundamental solutions and the radial basis functions for viscous laminar flow in wavy channel. (English) Zbl 1403.76154 Eng. Anal. Bound. Elem. 57, 58-65 (2015). MSC: 76M25 65N35 76D05 PDFBibTeX XMLCite \textit{J. A. Kołodziej} and \textit{J. K. Grabski}, Eng. Anal. Bound. Elem. 57, 58--65 (2015; Zbl 1403.76154) Full Text: DOI
Soghrati, Soheil; Mai, Weijie; Liang, Bowen; Buchheit, Rudolph G. A boundary collocation meshfree method for the treatment of Poisson problems with complex morphologies. (English) Zbl 1352.65577 J. Comput. Phys. 281, 225-236 (2015). MSC: 65N35 35J25 PDFBibTeX XMLCite \textit{S. Soghrati} et al., J. Comput. Phys. 281, 225--236 (2015; Zbl 1352.65577) Full Text: DOI
Jaworski, Andrzej Solution of the first biharmonic problem by the Trefftz method. (English) Zbl 1322.65107 ZAMM, Z. Angew. Math. Mech. 95, No. 3, 317-328 (2015). MSC: 65N30 35J40 PDFBibTeX XMLCite \textit{A. Jaworski}, ZAMM, Z. Angew. Math. Mech. 95, No. 3, 317--328 (2015; Zbl 1322.65107) Full Text: DOI
Karageorghis, Andreas The method of fundamental solutions for elliptic problems in circular domains with mixed boundary conditions. (English) Zbl 1308.65210 Numer. Algorithms 68, No. 1, 185-211 (2015). MSC: 65N80 35J05 35J40 65T50 PDFBibTeX XMLCite \textit{A. Karageorghis}, Numer. Algorithms 68, No. 1, 185--211 (2015; Zbl 1308.65210) Full Text: DOI
Zhang, Xueying; Tian, Haiyan; Chen, Wen Local method of approximate particular solutions for two-dimensional unsteady Burgers’ equations. (English) Zbl 1368.35239 Comput. Math. Appl. 66, No. 12, 2425-2432 (2014). MSC: 35Q53 35A35 76D05 PDFBibTeX XMLCite \textit{X. Zhang} et al., Comput. Math. Appl. 66, No. 12, 2425--2432 (2014; Zbl 1368.35239) Full Text: DOI
Heravi, Marjan Asadzadeh; Marin, Liviu; Sebu, Cristiana The method of fundamental solutions for complex electrical impedance tomography. (English) Zbl 1297.78009 Eng. Anal. Bound. Elem. 46, 126-139 (2014). MSC: 78A46 78M25 65N80 PDFBibTeX XMLCite \textit{M. A. Heravi} et al., Eng. Anal. Bound. Elem. 46, 126--139 (2014; Zbl 1297.78009) Full Text: DOI Link
Chen, Jeng-Tzong; Yang, Jheng-Lin; Lee, Ying-Te; Chang, Yu-Lung Formulation of the MFS for the two-dimensional Laplace equation with an added constant and constraint. (English) Zbl 1297.65194 Eng. Anal. Bound. Elem. 46, 96-107 (2014). MSC: 65N80 PDFBibTeX XMLCite \textit{J.-T. Chen} et al., Eng. Anal. Bound. Elem. 46, 96--107 (2014; Zbl 1297.65194) Full Text: DOI
Santos, W. J.; Santiago, J. A. F.; Telles, J. C. F. Optimal positioning of anodes and virtual sources in the design of cathodic protection systems using the method of fundamental solutions. (English) Zbl 1297.65197 Eng. Anal. Bound. Elem. 46, 67-74 (2014). MSC: 65N80 PDFBibTeX XMLCite \textit{W. J. Santos} et al., Eng. Anal. Bound. Elem. 46, 67--74 (2014; Zbl 1297.65197) Full Text: DOI
Gu, Yan; Chen, Wen; Fu, Zhuo-Jia; Zhang, Bo The singular boundary method: mathematical background and application in orthotropic elastic problems. (English) Zbl 1297.74145 Eng. Anal. Bound. Elem. 44, 152-160 (2014). MSC: 74S15 65N80 65N38 PDFBibTeX XMLCite \textit{Y. Gu} et al., Eng. Anal. Bound. Elem. 44, 152--160 (2014; Zbl 1297.74145) Full Text: DOI
Liu, Q. G.; Šarler, B. Non-singular method of fundamental solutions for anisotropic elasticity. (English) Zbl 1297.74019 Eng. Anal. Bound. Elem. 45, 68-78 (2014). MSC: 74B05 65N80 74S30 74E10 PDFBibTeX XMLCite \textit{Q. G. Liu} and \textit{B. Šarler}, Eng. Anal. Bound. Elem. 45, 68--78 (2014; Zbl 1297.74019) Full Text: DOI
Ahmadabadi, M. Nili; Arab, M.; Ghaini, F. M. Maalek The method of fundamental solutions for transient heat conduction in functionally graded materials: some special cases. (English) Zbl 1410.35239 J. Linear Topol. Algebra 2, No. 2, 117-127 (2013). MSC: 35Q79 80A20 65M80 65J20 PDFBibTeX XMLCite \textit{M. N. Ahmadabadi} et al., J. Linear Topol. Algebra 2, No. 2, 117--127 (2013; Zbl 1410.35239) Full Text: Link
Liu, Chein-Shan A multiple-scale Trefftz method for an incomplete Cauchy problem of biharmonic equation. (English) Zbl 1287.65103 Eng. Anal. Bound. Elem. 37, No. 11, 1445-1456 (2013). MSC: 65N20 65N35 PDFBibTeX XMLCite \textit{C.-S. Liu}, Eng. Anal. Bound. Elem. 37, No. 11, 1445--1456 (2013; Zbl 1287.65103) Full Text: DOI
Wen, Jin; Yamamoto, Masahiro; Wei, Ting Simultaneous determination of a time-dependent heat source and the initial temperature in an inverse heat conduction problem. (English) Zbl 1281.65126 Inverse Probl. Sci. Eng. 21, No. 3, 485-499 (2013). MSC: 65M32 35K05 35R30 80A20 80A23 65M80 PDFBibTeX XMLCite \textit{J. Wen} et al., Inverse Probl. Sci. Eng. 21, No. 3, 485--499 (2013; Zbl 1281.65126) Full Text: DOI
Karageorghis, Andreas; Lesnic, Daniel; Marin, Liviu A moving pseudo-boundary method of fundamental solutions for void detection. (English) Zbl 1268.65161 Numer. Methods Partial Differ. Equations 29, No. 3, 935-960 (2013). MSC: 65N80 35J05 65N30 65N21 PDFBibTeX XMLCite \textit{A. Karageorghis} et al., Numer. Methods Partial Differ. Equations 29, No. 3, 935--960 (2013; Zbl 1268.65161) Full Text: DOI Link
Tsai, Chia-Cheng Homotopy method of fundamental solutions for solving certain nonlinear partial differential equations. (English) Zbl 1352.65645 Eng. Anal. Bound. Elem. 36, No. 8, 1226-1234 (2012). MSC: 65N99 35C07 PDFBibTeX XMLCite \textit{C.-C. Tsai}, Eng. Anal. Bound. Elem. 36, No. 8, 1226--1234 (2012; Zbl 1352.65645) Full Text: DOI
Fu, Chu-Li; Zhang, Yuan-Xiang; Cheng, Hao; Ma, Yun-Jie Numerical analytic continuation on bounded domains. (English) Zbl 1352.65091 Eng. Anal. Bound. Elem. 36, No. 4, 493-504 (2012). MSC: 65E05 65J20 65N80 PDFBibTeX XMLCite \textit{C.-L. Fu} et al., Eng. Anal. Bound. Elem. 36, No. 4, 493--504 (2012; Zbl 1352.65091) Full Text: DOI
Boselli, F.; Obrist, D.; Kleiser, L. A multilayer method of fundamental solutions for Stokes flow problems. (English) Zbl 1277.65106 J. Comput. Phys. 231, No. 18, 6139-6158 (2012). MSC: 65N80 76D07 15A23 PDFBibTeX XMLCite \textit{F. Boselli} et al., J. Comput. Phys. 231, No. 18, 6139--6158 (2012; Zbl 1277.65106) Full Text: DOI
Li, Zi-Cai; Lu, Tzon-Tzer; Xie, G. Q. The method of fundamental solutions and its combinations for exterior problems. (English) Zbl 1245.65171 Eng. Anal. Bound. Elem. 36, No. 3, 394-403 (2012). MSC: 65N80 PDFBibTeX XMLCite \textit{Z.-C. Li} et al., Eng. Anal. Bound. Elem. 36, No. 3, 394--403 (2012; Zbl 1245.65171) Full Text: DOI
Wen, Jin A meshless method for reconstructing the heat source and partial initial temperature in heat condition. (English) Zbl 1244.65134 Inverse Probl. Sci. Eng. 19, No. 7, 1007-1022 (2011). MSC: 65M32 65M30 35K05 35R25 35R30 65M80 PDFBibTeX XMLCite \textit{J. Wen}, Inverse Probl. Sci. Eng. 19, No. 7, 1007--1022 (2011; Zbl 1244.65134) Full Text: DOI
Li, Zi-Cai; Lee, Ming-Gong; Chiang, John Y.; Liu, Ya Ping The Trefftz method using fundamental solutions for biharmonic equations. (English) Zbl 1222.65131 J. Comput. Appl. Math. 235, No. 15, 4350-4367 (2011). Reviewer: Costică Moroşanu (Iaşi) MSC: 65N80 PDFBibTeX XMLCite \textit{Z.-C. Li} et al., J. Comput. Appl. Math. 235, No. 15, 4350--4367 (2011; Zbl 1222.65131) Full Text: DOI
Wu, C. S.; Young, D. L.; Fan, C. M. Frequency response analyses in vibroacoustics using the method of fundamental solutions. (English) Zbl 1398.76173 Comput. Mech. 47, No. 5, 519-533 (2011). MSC: 76M25 76Q05 74S15 65N38 74S30 PDFBibTeX XMLCite \textit{C. S. Wu} et al., Comput. Mech. 47, No. 5, 519--533 (2011; Zbl 1398.76173) Full Text: DOI Link
Lee, Ming-Gong; Young, Lih-Jier; Li, Zi-Cai; Chu, Po-Chun Combined Trefftz methods of particular and fundamental solutions for corner and crack singularity of linear elastostatics. (English) Zbl 1267.74128 Eng. Anal. Bound. Elem. 34, No. 7, 632-654 (2010). MSC: 74S30 74G70 74R10 74B05 PDFBibTeX XMLCite \textit{M.-G. Lee} et al., Eng. Anal. Bound. Elem. 34, No. 7, 632--654 (2010; Zbl 1267.74128) Full Text: DOI
Li, Zi-Cai; Young, Lih-Jier; Huang, Hung-Tsai; Liu, Ya-Ping; Cheng, Alexander H.-D. Comparisons of fundamental solutions and particular solutions for Trefftz methods. (English) Zbl 1244.65187 Eng. Anal. Bound. Elem. 34, No. 3, 248-258 (2010). MSC: 65N35 65N15 65N12 65N30 PDFBibTeX XMLCite \textit{Z.-C. Li} et al., Eng. Anal. Bound. Elem. 34, No. 3, 248--258 (2010; Zbl 1244.65187) Full Text: DOI
Wei, T.; Zhou, D. Y. Convergence analysis for the Cauchy problem of Laplace’s equation by a regularized method of fundamental solutions. (English) Zbl 1213.65136 Adv. Comput. Math. 33, No. 4, 491-510 (2010). Reviewer: Robert Plato (Siegen) MSC: 65M80 65M30 65M70 65M12 35J05 PDFBibTeX XMLCite \textit{T. Wei} and \textit{D. Y. Zhou}, Adv. Comput. Math. 33, No. 4, 491--510 (2010; Zbl 1213.65136) Full Text: DOI
Marin, Liviu Treatment of singularities in the method of fundamental solutions for two-dimensional Helmholtz-type equations. (English) Zbl 1193.35223 Appl. Math. Modelling 34, No. 6, 1615-1633 (2010). MSC: 35Q74 35J05 74G70 PDFBibTeX XMLCite \textit{L. Marin}, Appl. Math. Modelling 34, No. 6, 1615--1633 (2010; Zbl 1193.35223) Full Text: DOI
Lesnic, D.; Zeb, A. The method of fundamental solutions for an inverse internal boundary value problem for the biharmonic equation. (English) Zbl 1267.65171 Int. J. Comput. Methods 6, No. 4 (2009). MSC: 65N21 65N80 PDFBibTeX XML Full Text: DOI
Young, D. L.; Lin, Y. C.; Fan, C. M.; Chiu, C. L. The method of fundamental solutions for solving incompressible Navier-Stokes problems. (English) Zbl 1244.76104 Eng. Anal. Bound. Elem. 33, No. 8-9, 1031-1044 (2009). MSC: 76M28 76D05 65M80 PDFBibTeX XMLCite \textit{D. L. Young} et al., Eng. Anal. Bound. Elem. 33, No. 8--9, 1031--1044 (2009; Zbl 1244.76104) Full Text: DOI
Ramachandran, P. A.; Gunjal, P. R. Comparison of boundary collocation methods for singular and non-singular axisymmetric heat transfer problems. (English) Zbl 1244.80012 Eng. Anal. Bound. Elem. 33, No. 5, 704-716 (2009). MSC: 80M15 80A20 65N80 65N35 PDFBibTeX XMLCite \textit{P. A. Ramachandran} and \textit{P. R. Gunjal}, Eng. Anal. Bound. Elem. 33, No. 5, 704--716 (2009; Zbl 1244.80012) Full Text: DOI
Chen, Jeng-Tzong; Lee, Ying-Te; Yu, Shang-Ru; Shieh, Shiang-Chih Equivalence between the Trefftz method and the method of fundamental solution for the annular Green’s function using the addition theorem and image concept. (English) Zbl 1244.65217 Eng. Anal. Bound. Elem. 33, No. 5, 678-688 (2009). MSC: 65N80 PDFBibTeX XMLCite \textit{J.-T. Chen} et al., Eng. Anal. Bound. Elem. 33, No. 5, 678--688 (2009; Zbl 1244.65217) Full Text: DOI
Smyrlis, Yiorgos-Sokratis Applicability and applications of the method of fundamental solutions. (English) Zbl 1198.65237 Math. Comput. 78, No. 267, 1399-1434 (2009). MSC: 65N35 35E05 41A30 35G15 35J40 65N38 PDFBibTeX XMLCite \textit{Y.-S. Smyrlis}, Math. Comput. 78, No. 267, 1399--1434 (2009; Zbl 1198.65237) Full Text: DOI
Ling, Leevan; Schaback, Robert An improved subspace selection algorithm for meshless collocation methods. (English) Zbl 1183.65153 Int. J. Numer. Methods Eng. 80, No. 13, 1623-1639 (2009). MSC: 65N35 PDFBibTeX XMLCite \textit{L. Ling} and \textit{R. Schaback}, Int. J. Numer. Methods Eng. 80, No. 13, 1623--1639 (2009; Zbl 1183.65153) Full Text: DOI
Ahmadabadi, M. Nili; Arab, M.; Ghaini, F. M. Maalek The method of fundamental solutions for the inverse space-dependent heat source problem. (English) Zbl 1180.80054 Eng. Anal. Bound. Elem. 33, No. 10, 1231-1235 (2009). MSC: 80A23 35R30 58J35 58J90 PDFBibTeX XMLCite \textit{M. N. Ahmadabadi} et al., Eng. Anal. Bound. Elem. 33, No. 10, 1231--1235 (2009; Zbl 1180.80054) Full Text: DOI
Tsiatas, G. C. A new Kirchhoff plate model based on a modified couple stress theory. (English) Zbl 1167.74489 Int. J. Solids Struct. 46, No. 13, 2757-2764 (2009). MSC: 74K20 PDFBibTeX XMLCite \textit{G. C. Tsiatas}, Int. J. Solids Struct. 46, No. 13, 2757--2764 (2009; Zbl 1167.74489) Full Text: DOI
Young, D. L.; Fan, C. M.; Hu, S. P.; Atluri, S. N. The Eulerian-Lagrangian method of fundamental solutions for two-dimensional unsteady Burgers’ equations. (English) Zbl 1244.76096 Eng. Anal. Bound. Elem. 32, No. 5, 395-412 (2008). MSC: 76M25 76D99 65M80 PDFBibTeX XMLCite \textit{D. L. Young} et al., Eng. Anal. Bound. Elem. 32, No. 5, 395--412 (2008; Zbl 1244.76096) Full Text: DOI
Yan, Liang; Fu, Chu-Li; Yang, Feng-Lian The method of fundamental solutions for the inverse heat source problem. (English) Zbl 1244.80026 Eng. Anal. Bound. Elem. 32, No. 3, 216-222 (2008). MSC: 80M25 80A23 80A20 65M80 PDFBibTeX XMLCite \textit{L. Yan} et al., Eng. Anal. Bound. Elem. 32, No. 3, 216--222 (2008; Zbl 1244.80026) Full Text: DOI
Gorzelańczyk, Piotr; Kołodziej, Jan A. Some remarks concerning the shape of the source contour with application of the method of fundamental solutions to elastic torsion of prismatic rods. (English) Zbl 1272.74623 Eng. Anal. Bound. Elem. 32, No. 1, 64-75 (2008). MSC: 74S30 74K10 65N80 PDFBibTeX XMLCite \textit{P. Gorzelańczyk} and \textit{J. A. Kołodziej}, Eng. Anal. Bound. Elem. 32, No. 1, 64--75 (2008; Zbl 1272.74623) Full Text: DOI
Pandit, Swapan K. On the use of compact streamfunction-velocity formulation of steady Navier-Stokes equations on geometries beyond rectangular. (English) Zbl 1203.65224 J. Sci. Comput. 36, No. 2, 219-242 (2008). MSC: 65N06 76D05 PDFBibTeX XMLCite \textit{S. K. Pandit}, J. Sci. Comput. 36, No. 2, 219--242 (2008; Zbl 1203.65224) Full Text: DOI
Karageorghis, A.; Lesnic, D. Steady-state nonlinear heat conduction in composite materials using the method of fundamental solutions. (English) Zbl 1194.74054 Comput. Methods Appl. Mech. Eng. 197, No. 33-40, 3122-3137 (2008). MSC: 74F05 74E30 80A20 65N80 65N35 65N38 65H10 PDFBibTeX XMLCite \textit{A. Karageorghis} and \textit{D. Lesnic}, Comput. Methods Appl. Mech. Eng. 197, No. 33--40, 3122--3137 (2008; Zbl 1194.74054) Full Text: DOI
Zeb, A.; Ingham, D. B.; Lesnic, D. The method of fundamental solutions for a biharmonic inverse boundary determination problem. (English) Zbl 1163.65078 Comput. Mech. 42, No. 3, 371-379 (2008). MSC: 65N21 35R30 35J40 65N35 PDFBibTeX XMLCite \textit{A. Zeb} et al., Comput. Mech. 42, No. 3, 371--379 (2008; Zbl 1163.65078) Full Text: DOI
Wei, Ting; Hon, Y. C.; Ling, Leevan Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators. (English) Zbl 1195.65206 Eng. Anal. Bound. Elem. 31, No. 4, 373-385 (2007). MSC: 65N80 PDFBibTeX XMLCite \textit{T. Wei} et al., Eng. Anal. Bound. Elem. 31, No. 4, 373--385 (2007; Zbl 1195.65206) Full Text: DOI
Chen, J. T.; Wu, C. S.; Lee, Y. T.; Chen, K. H. On the equivalence of the Trefftz method and method of fundamental solutions for Laplace and biharmonic equations. (English) Zbl 1125.65110 Comput. Math. Appl. 53, No. 6, 851-879 (2007). MSC: 65N38 35J05 35J40 PDFBibTeX XMLCite \textit{J. T. Chen} et al., Comput. Math. Appl. 53, No. 6, 851--879 (2007; Zbl 1125.65110) Full Text: DOI
Tsai, C. C.; Young, D. L.; Chen, C. W.; Fan, C. M. The method of fundamental solutions for eigenproblems in domains with and without interior holes. (English) Zbl 1149.35339 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 462, No. 2069, 1443-1466 (2006). MSC: 35J05 35P99 65N25 PDFBibTeX XMLCite \textit{C. C. Tsai} et al., Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 462, No. 2069, 1443--1466 (2006; Zbl 1149.35339) Full Text: DOI
Young, D. L.; Chiu, C. L.; Fan, C. M.; Tsai, C. C.; Lin, Y. C. Method of fundamental solutions for multidimensional Stokes equations by the dual-potential formulation. (English) Zbl 1106.76020 Eur. J. Mech., B, Fluids 25, No. 6, 877-893 (2006). MSC: 76D07 76M25 PDFBibTeX XMLCite \textit{D. L. Young} et al., Eur. J. Mech., B, Fluids 25, No. 6, 877--893 (2006; Zbl 1106.76020) Full Text: DOI
Mera, N. S. The method of fundamental solutions for the backward heat conduction problem. (English) Zbl 1194.80107 Inverse Probl. Sci. Eng. 13, No. 1, 65-78 (2005). MSC: 80A23 80A20 PDFBibTeX XMLCite \textit{N. S. Mera}, Inverse Probl. Sci. Eng. 13, No. 1, 65--78 (2005; Zbl 1194.80107) Full Text: DOI
Fam, George S. A.; Rashed, Youssef F. The method of fundamental solutions applied to 3D structures with body forces using particular solutions. (English) Zbl 1138.74419 Comput. Mech. 36, No. 4, 245-254 (2005). MSC: 74S30 74K10 74G99 PDFBibTeX XMLCite \textit{G. S. A. Fam} and \textit{Y. F. Rashed}, Comput. Mech. 36, No. 4, 245--254 (2005; Zbl 1138.74419) Full Text: DOI
Marin, L.; Lesnic, D. The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation. (English) Zbl 1088.35079 Math. Comput. Modelling 42, No. 3-4, 261-278 (2005). MSC: 35R25 35J40 65N21 35R30 31A30 35A08 PDFBibTeX XMLCite \textit{L. Marin} and \textit{D. Lesnic}, Math. Comput. Modelling 42, No. 3--4, 261--278 (2005; Zbl 1088.35079) Full Text: DOI
Marin, L. A meshless method for solving the Cauchy problem in three-dimensional elastostatics. (English) Zbl 1127.74014 Comput. Math. Appl. 50, No. 1-2, 73-92 (2005). MSC: 74G15 65F22 65N22 74B05 PDFBibTeX XMLCite \textit{L. Marin}, Comput. Math. Appl. 50, No. 1--2, 73--92 (2005; Zbl 1127.74014) Full Text: DOI
Marin, Liviu A meshless method for the numerical solution of the Cauchy problem associated with three-dimensional Helmholtz-type equations. (English) Zbl 1070.65115 Appl. Math. Comput. 165, No. 2, 355-374 (2005). MSC: 65N21 65N35 65N12 35R30 35J05 PDFBibTeX XMLCite \textit{L. Marin}, Appl. Math. Comput. 165, No. 2, 355--374 (2005; Zbl 1070.65115) Full Text: DOI
Fairweather, Graeme; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis A matrix decomposition MFS algorithm for axisymmetric biharmonic problems. (English) Zbl 1067.65135 Adv. Comput. Math. 23, No. 1-2, 55-71 (2005). MSC: 65N35 35J40 65F30 65T50 PDFBibTeX XMLCite \textit{G. Fairweather} et al., Adv. Comput. Math. 23, No. 1--2, 55--71 (2005; Zbl 1067.65135) Full Text: DOI
Li, Jichun Application of radial basis meshless methods to direct and inverse biharmonic boundary value problems. (English) Zbl 1067.65117 Commun. Numer. Methods Eng. 21, No. 4, 169-182 (2005). MSC: 65N21 31A25 35J40 35R30 31A30 65N35 PDFBibTeX XMLCite \textit{J. Li}, Commun. Numer. Methods Eng. 21, No. 4, 169--182 (2005; Zbl 1067.65117) Full Text: DOI
de Medeiros, Glauceny C.; Partridge, Paul W.; Brandão, Jorge O. The method of fundamental solutions with dual reciprocity for some problems in elasticity. (English) Zbl 1130.74482 Eng. Anal. Bound. Elem. 28, No. 5, 453-461 (2004). MSC: 74S15 74B05 PDFBibTeX XMLCite \textit{G. C. de Medeiros} et al., Eng. Anal. Bound. Elem. 28, No. 5, 453--461 (2004; Zbl 1130.74482) Full Text: DOI
Saavedra, I.; Power, H. Adaptive refinement scheme for the least-squares approach of the method of fundamental solution for three-dimensional harmonic problems. (English) Zbl 1074.65132 Eng. Anal. Bound. Elem. 28, No. 9, 1123-1133 (2004). MSC: 65N30 65N50 35J05 65F10 PDFBibTeX XMLCite \textit{I. Saavedra} and \textit{H. Power}, Eng. Anal. Bound. Elem. 28, No. 9, 1123--1133 (2004; Zbl 1074.65132) Full Text: DOI
Fairweather, Graeme; Karageorghis, Andreas; Martin, P. A. The method of fundamental solutions for scattering and radiation problems. (English) Zbl 1060.76649 Eng. Anal. Bound. Elem. 27, No. 7, 759-769 (2003). MSC: 76Q05 76M25 76-02 PDFBibTeX XMLCite \textit{G. Fairweather} et al., Eng. Anal. Bound. Elem. 27, No. 7, 759--769 (2003; Zbl 1060.76649) Full Text: DOI
Chen, C. S.; Kuhn, G.; Li, J.; Mishuris, G. Radial basis functions for solving near singular Poisson problems. (English) Zbl 1018.65131 Commun. Numer. Methods Eng. 19, No. 5, 333-347 (2003). MSC: 65N35 35J05 PDFBibTeX XMLCite \textit{C. S. Chen} et al., Commun. Numer. Methods Eng. 19, No. 5, 333--347 (2003; Zbl 1018.65131) Full Text: DOI
Sladek, J.; Sladek, V.; Mang, H. A. Meshless local boundary integral equation method for simply supported and clamped plates resting on elastic foundation. (English) Zbl 1083.74603 Comput. Methods Appl. Mech. Eng. 191, No. 51-52, 5943-5959 (2002). MSC: 74S15 74K20 PDFBibTeX XMLCite \textit{J. Sladek} et al., Comput. Methods Appl. Mech. Eng. 191, No. 51--52, 5943--5959 (2002; Zbl 1083.74603) Full Text: DOI
Ramachandran, P. A. Method of fundamental solutions: Singular value decomposition analysis. (English) Zbl 1016.65095 Commun. Numer. Methods Eng. 18, No. 11, 789-801 (2002). MSC: 65N38 35J05 65N35 65N12 65N15 PDFBibTeX XMLCite \textit{P. A. Ramachandran}, Commun. Numer. Methods Eng. 18, No. 11, 789--801 (2002; Zbl 1016.65095) Full Text: DOI
Balakrishnan, K.; Ramachandran, P. A. The method of fundamental solutions for linear diffusion-reaction equations. (English) Zbl 1042.35569 Math. Comput. Modelling 31, No. 2-3, 221-237 (2000). MSC: 35K57 35A08 65N35 PDFBibTeX XMLCite \textit{K. Balakrishnan} and \textit{P. A. Ramachandran}, Math. Comput. Modelling 31, No. 2--3, 221--237 (2000; Zbl 1042.35569) Full Text: DOI