- Referenced in 189 articles
- Reduced basis methods for partial differential equations. An introduction. This book provides a basic introduction ... reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs ... presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses ... priori and a posteriori error analysis. Reduced basis methods for partial differential equations. An introduction...
- Referenced in 12 articles
- modelling techniques (and, in particular, certified reduced basis method and Proper Orthogonal Decomposition-Galerkin methods ... suited for an introductory course on reduced basis methods and reduced order modelling, thanks ... employed in several doctoral courses on ”Reduced Basis Methods for Computational Mechanics”. RBniCS can also ... availability of several reduced order methods (such as reduced basis and proper orthogonal decomposition...
- Referenced in 798 articles
- reduces to a variant of the Lanczos process called the Implicitly Restarted Lanczos Method (IRLM ... storage is required. A set of Schur basis vectors for the desired k-dimensional eigen...
- Referenced in 14 articles
- focus lies on the application of reduced basis methods to parameterized partial differential equations...
- Referenced in 265 articles
- darch package is build on the basis of the code from G. E. Hinton ... deep architectures) and train them with the method introduced by the publications ”A fast learning ... Hinton, S. Osindero, Y. W. Teh) and ”Reducing the dimensionality of data with neural networks...
- Referenced in 11 articles
- parallelism offered by multiscale and uncertainty quantification methods where we have focused on the adaptive ... combination of local reduced basis multiscale methods and the multilevel Monte-Carlo algorithm. Finally, some...
- Referenced in 165 articles
- CONOPT is a generalized reduced-gradient (GRG) algorithm for solving large-scale nonlinear programs involving ... with the popular methods based on sequential linearized subproblems forms the basis for discussions...
- Referenced in 22 articles
- correlated coupled-cluster methods yield CCSD(T) results with near basis set limit accuracy ... already with double-? or triple-? basis sets, thus reducing the computational effort for calculations ... orders of magnitude. Using local electron correlation methods, which significantly reduce the increase...
- Referenced in 31 articles
- method (PUM). Compared to classical finite element methods (FEM), a PUM can directly utilize user ... basis functions in order improve the approximation properties of the model and to reduce ... Schweitzer. A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations, Volume...
- Referenced in 18 articles
- method-of-lines approach, with collocation in the space variable to reduce the problem ... principal components: the basis functions employed in the collocation; the method used to solve...
- Referenced in 36 articles
- solvers can be of great value in reducing the often high computational cost of simulations ... reﬁnement methods (CHARMS). The basic principle of our approach is to reﬁne basis functions...
- Referenced in 6 articles
- LINA01: A REDUCE program for the normalization of polynomial Hamiltonians. The program LINA01 is proposed ... basis of Lie canonical transformation method. The program package of LINA01 is written on REDUCE...
- Referenced in 7 articles
- conditioned. The Matlab Radial Basis Function toolbox features a regularization method for the ill-conditioned ... symmetry exploitation for the purpose of reducing flop counts of the associated numerical linear algebra...
- Referenced in 8 articles
- method overlaps simplex iterations on different processors. Candidates to enter the basis are tentatively selected ... using reduced costs which may be out of date. Later, the up-to-date reduced...
- Referenced in 6 articles
- Discretization methods implementing grid-based discretization operators of partial differential equations. (M2) Reduced basis generation...
- Referenced in 4 articles
- guards provides a powerful tool for heuristically reducing the combinatorial explosion of cases: equivalent, redundant ... basis of simplification knowledge on the logical side. The method described in this paper ... implemented in the REDUCE package GUARDIAN, which is freely available...
- Referenced in 18 articles
- uses a two-phase, active-set, reduced-Hessian method. It is most efficient on problems ... SQOPT uses stable numerical methods throughout and includes a reliable basis package (for maintaining sparse...
- Referenced in 13 articles
- compressible problems is not trivial. Therefore, several basis function formulations (incompressible and compressible, with ... finite volume (MSFV) and finite element (MSFE) methods. Finally, in order to resolve high-frequency ... smoother stages are employed. In order to reduce computational expense, the C-AMS operators (prolongation...
- Referenced in 2 articles
- basis to a multilevel mesh. In this method, Poisson’s equation is solved ... flux is found by using loop-tree basis based on Helmholtz decomposition of field; second ... speed, we propose to use hierarchical loop basis to construct a multilevel system ... noticeably reduced. Numerical examples are presented to demonstrate the efficiency of the proposed method...
- Referenced in 5 articles
- well-known complex variable boundary element method (CVBEM) is extended for using collocation points ... advancement is determining values of the CVBEM basis function complex coefficients by collocation at evaluation ... computer program Mathematica, in order to reduce programming requirements and to take advantage of Mathematica...