Jahanbin, Ramin; Rahman, Sharif Stochastic isogeometric analysis on arbitrary multipatch domains by spline dimensional decomposition. (English) Zbl 1507.65042 Comput. Methods Appl. Mech. Eng. 393, Article ID 114813, 36 p. (2022). MSC: 65D07 65C05 65N30 PDFBibTeX XMLCite \textit{R. Jahanbin} and \textit{S. Rahman}, Comput. Methods Appl. Mech. Eng. 393, Article ID 114813, 36 p. (2022; Zbl 1507.65042) Full Text: DOI
Harbrecht, Helmut; Multerer, Michael; von Rickenbach, Remo Isogeometric shape optimization of periodic structures in three dimensions. (English) Zbl 1507.49034 Comput. Methods Appl. Mech. Eng. 391, Article ID 114552, 16 p. (2022). MSC: 49Q10 49K20 74P20 74Q05 PDFBibTeX XMLCite \textit{H. Harbrecht} et al., Comput. Methods Appl. Mech. Eng. 391, Article ID 114552, 16 p. (2022; Zbl 1507.49034) Full Text: DOI arXiv
Dölz, Jürgen; Harbrecht, Helmut; Jerez-Hanckes, Carlos; Multerer, Michael Isogeometric multilevel quadrature for forward and inverse random acoustic scattering. (English) Zbl 1507.74529 Comput. Methods Appl. Mech. Eng. 388, Article ID 114242, 18 p. (2022). MSC: 74S15 65N38 65D32 74J20 76Q05 PDFBibTeX XMLCite \textit{J. Dölz} et al., Comput. Methods Appl. Mech. Eng. 388, Article ID 114242, 18 p. (2022; Zbl 1507.74529) Full Text: DOI arXiv
Gerasimov, Tymofiy; Römer, Ulrich; Vondřejc, Jaroslav; Matthies, Hermann G.; De Lorenzis, Laura Stochastic phase-field modeling of brittle fracture: computing multiple crack patterns and their probabilities. (English) Zbl 1506.74351 Comput. Methods Appl. Mech. Eng. 372, Article ID 113353, 29 p. (2020). MSC: 74R10 74S05 65N30 74S60 PDFBibTeX XMLCite \textit{T. Gerasimov} et al., Comput. Methods Appl. Mech. Eng. 372, Article ID 113353, 29 p. (2020; Zbl 1506.74351) Full Text: DOI arXiv
Jahanbin, Ramin; Rahman, Sharif Stochastic isogeometric analysis in linear elasticity. (English) Zbl 1442.74253 Comput. Methods Appl. Mech. Eng. 364, Article ID 112928, 38 p. (2020). MSC: 74S70 74S60 65N30 65D07 65N75 74B05 74S22 PDFBibTeX XMLCite \textit{R. Jahanbin} and \textit{S. Rahman}, Comput. Methods Appl. Mech. Eng. 364, Article ID 112928, 38 p. (2020; Zbl 1442.74253) Full Text: DOI
Botti, Michele; Di Pietro, Daniele A.; Le Maître, Olivier; Sochala, Pierre Numerical approximation of poroelasticity with random coefficients using polynomial chaos and hybrid high-order methods. (English) Zbl 1442.74063 Comput. Methods Appl. Mech. Eng. 361, Article ID 112736, 25 p. (2020). MSC: 74F10 74S25 74S60 PDFBibTeX XMLCite \textit{M. Botti} et al., Comput. Methods Appl. Mech. Eng. 361, Article ID 112736, 25 p. (2020; Zbl 1442.74063) Full Text: DOI arXiv
Feng, Yuan; Gao, Wei; Wu, Di; Tin-Loi, Francis Machine learning aided stochastic elastoplastic analysis. (English) Zbl 1442.74041 Comput. Methods Appl. Mech. Eng. 357, Article ID 112576, 31 p. (2019). MSC: 74C05 65C30 65N30 PDFBibTeX XMLCite \textit{Y. Feng} et al., Comput. Methods Appl. Mech. Eng. 357, Article ID 112576, 31 p. (2019; Zbl 1442.74041) Full Text: DOI
Torii, André Jacomel Robust compliance-based topology optimization: a discussion on physical consistency. (English) Zbl 1441.74170 Comput. Methods Appl. Mech. Eng. 352, 110-136 (2019). MSC: 74P15 PDFBibTeX XMLCite \textit{A. J. Torii}, Comput. Methods Appl. Mech. Eng. 352, 110--136 (2019; Zbl 1441.74170) Full Text: DOI
Rahman, Sharif A Galerkin isogeometric method for Karhunen-Loève approximation of random fields. (English) Zbl 1440.65228 Comput. Methods Appl. Mech. Eng. 338, 533-561 (2018). MSC: 65N30 65R20 45C05 65D07 PDFBibTeX XMLCite \textit{S. Rahman}, Comput. Methods Appl. Mech. Eng. 338, 533--561 (2018; Zbl 1440.65228) Full Text: DOI arXiv
Eigel, Martin; Neumann, Johannes; Schneider, Reinhold; Wolf, Sebastian Risk averse stochastic structural topology optimization. (English) Zbl 1440.74291 Comput. Methods Appl. Mech. Eng. 334, 470-482 (2018). MSC: 74P15 35R60 47B80 60H35 65N12 65N75 PDFBibTeX XMLCite \textit{M. Eigel} et al., Comput. Methods Appl. Mech. Eng. 334, 470--482 (2018; Zbl 1440.74291) Full Text: DOI
Li, Keyan; Gao, Wei; Wu, Di; Song, Chongmin; Chen, Taicong Spectral stochastic isogeometric analysis of linear elasticity. (English) Zbl 1439.74441 Comput. Methods Appl. Mech. Eng. 332, 157-190 (2018). MSC: 74S05 65N30 65D07 65N75 74B05 PDFBibTeX XMLCite \textit{K. Li} et al., Comput. Methods Appl. Mech. Eng. 332, 157--190 (2018; Zbl 1439.74441) Full Text: DOI
Stavroulakis, G.; Giovanis, D. G.; Papadopoulos, V.; Papadrakakis, M. A GPU domain decomposition solution for spectral stochastic finite element method. (English) Zbl 1439.74467 Comput. Methods Appl. Mech. Eng. 327, 392-410 (2017). MSC: 74S05 74S60 65N75 65N30 65Y10 PDFBibTeX XMLCite \textit{G. Stavroulakis} et al., Comput. Methods Appl. Mech. Eng. 327, 392--410 (2017; Zbl 1439.74467) Full Text: DOI
Wu, Di; Gao, Wei Hybrid uncertain static analysis with random and interval fields. (English) Zbl 1439.74496 Comput. Methods Appl. Mech. Eng. 315, 222-246 (2017). MSC: 74S60 65N75 65G30 74A10 PDFBibTeX XMLCite \textit{D. Wu} and \textit{W. Gao}, Comput. Methods Appl. Mech. Eng. 315, 222--246 (2017; Zbl 1439.74496) Full Text: DOI
Ilango, Santhosh Jude Joseph; Sarkar, Sunetra An efficient stochastic framework to propagate the effect of the random solid-pore geometry of porous media on the pore-scale flow. (English) Zbl 1439.74110 Comput. Methods Appl. Mech. Eng. 315, 73-99 (2017). MSC: 74F10 76S05 65C30 76M35 PDFBibTeX XMLCite \textit{S. J. J. Ilango} and \textit{S. Sarkar}, Comput. Methods Appl. Mech. Eng. 315, 73--99 (2017; Zbl 1439.74110) Full Text: DOI
Guignard, Diane; Nobile, Fabio; Picasso, Marco A posteriori error estimation for the steady Navier-Stokes equations in random domains. (English) Zbl 1439.76022 Comput. Methods Appl. Mech. Eng. 313, 483-511 (2017). MSC: 76D06 65N15 65N30 76M10 PDFBibTeX XMLCite \textit{D. Guignard} et al., Comput. Methods Appl. Mech. Eng. 313, 483--511 (2017; Zbl 1439.76022) Full Text: DOI
Pettersson, Per; Tchelepi, Hamdi A. Stochastic Galerkin framework with locally reduced bases for nonlinear two-phase transport in heterogeneous formations. (English) Zbl 1439.65129 Comput. Methods Appl. Mech. Eng. 310, 367-387 (2016). MSC: 65M75 35F31 60H35 65M60 65T60 PDFBibTeX XMLCite \textit{P. Pettersson} and \textit{H. A. Tchelepi}, Comput. Methods Appl. Mech. Eng. 310, 367--387 (2016; Zbl 1439.65129) Full Text: DOI arXiv
Martínez-Frutos, Jesús; Herrero-Pérez, David Large-scale robust topology optimization using multi-GPU systems. (English) Zbl 1439.74291 Comput. Methods Appl. Mech. Eng. 311, 393-414 (2016). MSC: 74P15 PDFBibTeX XMLCite \textit{J. Martínez-Frutos} and \textit{D. Herrero-Pérez}, Comput. Methods Appl. Mech. Eng. 311, 393--414 (2016; Zbl 1439.74291) Full Text: DOI
Wu, F.; Zhong, W. X. A modified stochastic perturbation method for stochastic hyperbolic heat conduction problems. (English) Zbl 1425.74021 Comput. Methods Appl. Mech. Eng. 305, 739-758 (2016). MSC: 74A15 74S60 35R60 65M75 PDFBibTeX XMLCite \textit{F. Wu} and \textit{W. X. Zhong}, Comput. Methods Appl. Mech. Eng. 305, 739--758 (2016; Zbl 1425.74021) Full Text: DOI
Erhel, J.; Mghazli, Z.; Oumouni, M. An adaptive sparse grid method for elliptic PDEs with stochastic coefficients. (English) Zbl 1425.65198 Comput. Methods Appl. Mech. Eng. 297, 392-407 (2015). MSC: 65N35 65C05 65N75 35J25 35R60 PDFBibTeX XMLCite \textit{J. Erhel} et al., Comput. Methods Appl. Mech. Eng. 297, 392--407 (2015; Zbl 1425.65198) Full Text: DOI HAL
Wang, Hong; Ren, Yongqiang; Jia, Jinhong; Celia, Michael A. A probabilistic collocation eulerian-Lagrangian localized adjoint method on sparse grids for assessing \(\operatorname{CO}_2\) leakage through wells in randomly heterogeneous porous media. (English) Zbl 1423.76375 Comput. Methods Appl. Mech. Eng. 292, 35-53 (2015). MSC: 76M28 65M70 65M75 74F10 76S05 PDFBibTeX XMLCite \textit{H. Wang} et al., Comput. Methods Appl. Mech. Eng. 292, 35--53 (2015; Zbl 1423.76375) Full Text: DOI
Audouze, Christophe; Nair, Prasanth B. Anchored ANOVA Petrov-Galerkin projection schemes for parabolic stochastic partial differential equations. (English) Zbl 1425.65016 Comput. Methods Appl. Mech. Eng. 276, 362-395 (2014). MSC: 65C30 65M60 60H15 60H35 65M75 PDFBibTeX XMLCite \textit{C. Audouze} and \textit{P. B. Nair}, Comput. Methods Appl. Mech. Eng. 276, 362--395 (2014; Zbl 1425.65016) Full Text: DOI
Rosseel, Eveline; Wells, Garth N. Optimal control with stochastic PDE constraints and uncertain controls. (English) Zbl 1243.49034 Comput. Methods Appl. Mech. Eng. 213-216, 152-167 (2012). MSC: 49K45 49M25 60H15 PDFBibTeX XMLCite \textit{E. Rosseel} and \textit{G. N. Wells}, Comput. Methods Appl. Mech. Eng. 213--216, 152--167 (2012; Zbl 1243.49034) Full Text: DOI arXiv
Tootkaboni, Mazdak; Asadpoure, Alireza; Guest, James K. Topology optimization of continuum structures under uncertainty - A polynomial chaos approach. (English) Zbl 1239.74081 Comput. Methods Appl. Mech. Eng. 201-204, 263-275 (2012). MSC: 74P15 74S60 65N30 65N75 PDFBibTeX XMLCite \textit{M. Tootkaboni} et al., Comput. Methods Appl. Mech. Eng. 201--204, 263--275 (2012; Zbl 1239.74081) Full Text: DOI
Tootkaboni, M.; Graham-Brady, L.; Schafer, B. W. Geometrically nonlinear behavior of structural systems with random material property: an asymptotic spectral stochastic approach. (English) Zbl 1229.74159 Comput. Methods Appl. Mech. Eng. 198, No. 37-40, 3173-3185 (2009). MSC: 74S60 74K10 74E35 PDFBibTeX XMLCite \textit{M. Tootkaboni} et al., Comput. Methods Appl. Mech. Eng. 198, No. 37--40, 3173--3185 (2009; Zbl 1229.74159) Full Text: DOI
Wan, Xiaoliang; Karniadakis, George Em Solving elliptic problems with non-Gaussian spatially-dependent random coefficients. (English) Zbl 1227.65014 Comput. Methods Appl. Mech. Eng. 198, No. 21-26, 1985-1995 (2009). MSC: 65C30 PDFBibTeX XMLCite \textit{X. Wan} and \textit{G. E. Karniadakis}, Comput. Methods Appl. Mech. Eng. 198, No. 21--26, 1985--1995 (2009; Zbl 1227.65014) Full Text: DOI
Chen, Nian Zhong; Soares, C. Guedes Spectral stochastic finite element analysis for laminated composite plates. (English) Zbl 1194.74378 Comput. Methods Appl. Mech. Eng. 197, No. 51-52, 4830-4839 (2008). MSC: 74S05 74S25 74S60 74K20 74E30 PDFBibTeX XMLCite \textit{N. Z. Chen} and \textit{C. G. Soares}, Comput. Methods Appl. Mech. Eng. 197, No. 51--52, 4830--4839 (2008; Zbl 1194.74378) Full Text: DOI
Nouy, A.; Clément, A.; Schoefs, F.; Moës, N. An extended stochastic finite element method for solving stochastic partial differential equations on random domains. (English) Zbl 1194.74457 Comput. Methods Appl. Mech. Eng. 197, No. 51-52, 4663-4682 (2008). MSC: 74S05 74S60 74E35 65C30 PDFBibTeX XMLCite \textit{A. Nouy} et al., Comput. Methods Appl. Mech. Eng. 197, No. 51--52, 4663--4682 (2008; Zbl 1194.74457) Full Text: DOI
Chamoin, Ludovic; Oden, J. T.; Prudhomme, Serge A stochastic coupling method for atomic-to-continuum MonteCarlo simulations. (English) Zbl 1194.74548 Comput. Methods Appl. Mech. Eng. 197, No. 43-44, 3530-3546 (2008). MSC: 74S60 74A25 PDFBibTeX XMLCite \textit{L. Chamoin} et al., Comput. Methods Appl. Mech. Eng. 197, No. 43--44, 3530--3546 (2008; Zbl 1194.74548) Full Text: DOI
Dostert, P.; Efendiev, Y.; Hou, T. Y. Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification. (English) Zbl 1194.76112 Comput. Methods Appl. Mech. Eng. 197, No. 43-44, 3445-3455 (2008). MSC: 76M10 76S05 76M35 PDFBibTeX XMLCite \textit{P. Dostert} et al., Comput. Methods Appl. Mech. Eng. 197, No. 43--44, 3445--3455 (2008; Zbl 1194.76112) Full Text: DOI
Lin, Guang; Su, Chau-Hsing; Karniadakis, G. E. Stochastic modeling of random roughness in shock scattering problems: theory and simulations. (English) Zbl 1194.76099 Comput. Methods Appl. Mech. Eng. 197, No. 43-44, 3420-3434 (2008). MSC: 76L05 76M35 PDFBibTeX XMLCite \textit{G. Lin} et al., Comput. Methods Appl. Mech. Eng. 197, No. 43--44, 3420--3434 (2008; Zbl 1194.76099) Full Text: DOI
Hasselman, Timothy; Lloyd, George A top-down approach to calibration, validation, uncertainty quantification and predictive accuracy assessment. (English) Zbl 1388.74123 Comput. Methods Appl. Mech. Eng. 197, No. 29-32, 2596-2606 (2008). MSC: 74S30 PDFBibTeX XMLCite \textit{T. Hasselman} and \textit{G. Lloyd}, Comput. Methods Appl. Mech. Eng. 197, No. 29--32, 2596--2606 (2008; Zbl 1388.74123) Full Text: DOI
Ghanem, Roger G.; Doostan, Alireza; Red-Horse, John A probabilistic construction of model validation. (English) Zbl 1213.74007 Comput. Methods Appl. Mech. Eng. 197, No. 29-32, 2585-2595 (2008). MSC: 74-05 PDFBibTeX XMLCite \textit{R. G. Ghanem} et al., Comput. Methods Appl. Mech. Eng. 197, No. 29--32, 2585--2595 (2008; Zbl 1213.74007) Full Text: DOI
Doostan, Alireza; Ghanem, Roger G.; Red-Horse, John Stochastic model reduction for chaos representations. (English) Zbl 1173.74411 Comput. Methods Appl. Mech. Eng. 196, No. 37-40, 3951-3966 (2007). MSC: 74S05 74E35 PDFBibTeX XMLCite \textit{A. Doostan} et al., Comput. Methods Appl. Mech. Eng. 196, No. 37--40, 3951--3966 (2007; Zbl 1173.74411) Full Text: DOI
Matthies, Hermann G.; Keese, Andreas Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations. (English) Zbl 1088.65002 Comput. Methods Appl. Mech. Eng. 194, No. 12-16, 1295-1331 (2005). Reviewer: Dominique Lepingle (Orléans) MSC: 65C30 60H15 35R60 60H35 35J25 35J65 65N12 65C05 PDFBibTeX XMLCite \textit{H. G. Matthies} and \textit{A. Keese}, Comput. Methods Appl. Mech. Eng. 194, No. 12--16, 1295--1331 (2005; Zbl 1088.65002) Full Text: DOI Link
Le Maître, O. P.; Knio, O. M.; Debusschere, B. J.; Najm, H. N.; Ghanem, R. G. A multigrid solver for two-dimensional stochastic diffusion equations. (English) Zbl 1037.65007 Comput. Methods Appl. Mech. Eng. 192, No. 41-42, 4723-4744 (2003). MSC: 65C30 65M55 65M06 65M12 60H15 35R60 60H35 PDFBibTeX XMLCite \textit{O. P. Le Maître} et al., Comput. Methods Appl. Mech. Eng. 192, No. 41--42, 4723--4744 (2003; Zbl 1037.65007) Full Text: DOI
Park, H. M.; Sung, M. C. Sequential solution of a three-dimensional inverse radiation problem. (English) Zbl 1044.80005 Comput. Methods Appl. Mech. Eng. 192, No. 33-34, 3689-3704 (2003). Reviewer: Messoud A. Efendiev (Berlin) MSC: 80A23 80A20 78A40 PDFBibTeX XMLCite \textit{H. M. Park} and \textit{M. C. Sung}, Comput. Methods Appl. Mech. Eng. 192, No. 33--34, 3689--3704 (2003; Zbl 1044.80005) Full Text: DOI
Park, H. M.; Shin, H. J. Empirical reduction of modes for the shape identification problems of heat conduction systems. (English) Zbl 1032.80008 Comput. Methods Appl. Mech. Eng. 192, No. 15, 1893-1908 (2003). MSC: 80M25 80A23 PDFBibTeX XMLCite \textit{H. M. Park} and \textit{H. J. Shin}, Comput. Methods Appl. Mech. Eng. 192, No. 15, 1893--1908 (2003; Zbl 1032.80008) Full Text: DOI
Xiu, Dongbin; Karniadakis, George Em Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. (English) Zbl 1016.65001 Comput. Methods Appl. Mech. Eng. 191, No. 43, 4927-4948 (2002). MSC: 65C30 35R60 35J05 65C05 60H15 65N30 65F10 60H35 PDFBibTeX XMLCite \textit{D. Xiu} and \textit{G. E. Karniadakis}, Comput. Methods Appl. Mech. Eng. 191, No. 43, 4927--4948 (2002; Zbl 1016.65001) Full Text: DOI
Park, H. M.; Lee, W. J. Feedback control of natural convection. (English) Zbl 1009.76022 Comput. Methods Appl. Mech. Eng. 191, No. 8-10, 1013-1028 (2001). MSC: 76D55 76R10 80A20 PDFBibTeX XMLCite \textit{H. M. Park} and \textit{W. J. Lee}, Comput. Methods Appl. Mech. Eng. 191, No. 8--10, 1013--1028 (2001; Zbl 1009.76022) Full Text: DOI
Deb, Manas K.; Babuška, Ivo M.; Oden, J. Tinsley Solution of stochastic partial differential equations using Galerkin finite element techniques. (English) Zbl 1075.65006 Comput. Methods Appl. Mech. Eng. 190, No. 48, 6359-6372 (2001). MSC: 65C30 65N30 PDFBibTeX XMLCite \textit{M. K. Deb} et al., Comput. Methods Appl. Mech. Eng. 190, No. 48, 6359--6372 (2001; Zbl 1075.65006) Full Text: DOI
Akiba, Hiroshi; Yagawa, Genki Recursive distribution method for probabilistic structural integrity analysis. (English) Zbl 0955.74078 Comput. Methods Appl. Mech. Eng. 168, No. 1-4, 135-154 (1999). MSC: 74S30 74A45 60H30 PDFBibTeX XMLCite \textit{H. Akiba} and \textit{G. Yagawa}, Comput. Methods Appl. Mech. Eng. 168, No. 1--4, 135--154 (1999; Zbl 0955.74078) Full Text: DOI
Ghanem, Roger Ingredients for a general purpose stochastic finite elements implementation. (English) Zbl 0943.65008 Comput. Methods Appl. Mech. Eng. 168, No. 1-4, 19-34 (1999). Reviewer: W.Grecksch (Halle) MSC: 65C30 60H15 PDFBibTeX XMLCite \textit{R. Ghanem}, Comput. Methods Appl. Mech. Eng. 168, No. 1--4, 19--34 (1999; Zbl 0943.65008) Full Text: DOI
Ghanem, Roger Probabilistic characterization of transport in heterogeneous media. (English) Zbl 0954.76079 Comput. Methods Appl. Mech. Eng. 158, No. 3-4, 199-220 (1998). MSC: 76M35 76S05 PDFBibTeX XMLCite \textit{R. Ghanem}, Comput. Methods Appl. Mech. Eng. 158, No. 3--4, 199--220 (1998; Zbl 0954.76079) Full Text: DOI