Results 1  10
of
23
deal.II – a general purpose object oriented finite element library
 ACM TRANS. MATH. SOFTW
"... An overview of the software design and data abstraction decisions chosen for deal.II, a general purpose finite element library written in C++, is given. The library uses advanced objectoriented and data encapsulation techniques to break finite element implementations into smaller blocks that can be ..."
Abstract

Cited by 104 (28 self)
 Add to MetaCart
An overview of the software design and data abstraction decisions chosen for deal.II, a general purpose finite element library written in C++, is given. The library uses advanced objectoriented and data encapsulation techniques to break finite element implementations into smaller blocks that can be arranged to fit users requirements. Through this approach, deal.II supports a large number of different applications covering a wide range of scientific areas, programming methodologies, and applicationspecific algorithms, without imposing a rigid framework into which they have to fit. A judicious use of programming techniques allows to avoid the computational costs frequently associated with abstract objectoriented class libraries. The paper presents a detailed description of the abstractions chosen for defining geometric information of meshes and the handling of degrees of freedom associated with finite element spaces, as well as of linear algebra, input/output capabilities and of interfaces to other software, such as visualization tools. Finally, some results obtained with applications built atop deal.II are shown to demonstrate the powerful capabilities of this toolbox.
deal.II  A GeneralPurpose ObjectOriented Finite Element Library
, 2007
"... An overview of the software design and data abstraction decisions chosen for deal.II, a general purpose finite element library written in C++, is given. The library uses advanced objectoriented and data encapsulation techniques to break finite element implementations into smaller blocks that can be ..."
Abstract

Cited by 27 (1 self)
 Add to MetaCart
An overview of the software design and data abstraction decisions chosen for deal.II, a general purpose finite element library written in C++, is given. The library uses advanced objectoriented and data encapsulation techniques to break finite element implementations into smaller blocks that can be arranged to fit users requirements. Through this approach, deal.II supports a large number of different applications covering a wide range of scientific areas, programming methodologies, and applicationspecific algorithms, without imposing a rigid framework into which they have to fit. A judicious use of programming techniques allows us to avoid the computational costs frequently associated with abstract objectoriented class libraries. The paper presents a detailed description of the abstractions chosen for defining geometric information of meshes and the handling of degrees of freedom associated with finite element spaces, as well as of linear algebra, input/output capabilities and of interfaces to other software, such as visualization tools. Finally, some results obtained with applications built atop deal.II are shown to demonstrate the powerful capabilities of this toolbox.
Adaptive finite element methods for the solution of inverse problems
 in optical tomography, Inverse Problems, accepted
, 2008
"... in optical tomography ..."
(Show Context)
MODEL VARIATIONAL INVERSE PROBLEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS∗
, 2011
"... Abstract. We discuss solution methods for inverse problems, in which the unknown parameters are connected to the measurements through a partial differential equation (PDE). Various features that commonly arise in these problems, such as inversions for a coefficient field, for the initial condition ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
(Show Context)
Abstract. We discuss solution methods for inverse problems, in which the unknown parameters are connected to the measurements through a partial differential equation (PDE). Various features that commonly arise in these problems, such as inversions for a coefficient field, for the initial condition in a timedependent problem, and for source terms are being studied in the context of three model problems. These problems cover distributed, boundary, as well as point measurements, different types of regularizations, linear and nonlinear PDEs, and bound constraints on the parameter field. The derivations of the optimality conditions are shown and efficient solution algorithms are presented. Short implementations of these algorithms in a generic finite element toolkit demonstrate practical strategies for solving inverse problems with PDEs. The complete implementations are made available to allow the reader to experiment with the model problems and to extend them as needed.
Threedimensional hadaptivity for the multigroup neutron diffusion equations
 Progr. Nucl. Energy
"... Adaptive mesh refinement (AMR) has been shown to allow solving partial differential equations to significantly higher accuracy at reduced numerical cost. This paper presents a stateoftheart AMR algorithm applied to the multigroup neutron diffusion equation for reactor applications. In order to fo ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Adaptive mesh refinement (AMR) has been shown to allow solving partial differential equations to significantly higher accuracy at reduced numerical cost. This paper presents a stateoftheart AMR algorithm applied to the multigroup neutron diffusion equation for reactor applications. In order to follow the physics closely, energy groupdependent meshes are employed. The method is formulated using finite elements of any order, for any number of energy groups. The spatial error distribution is assessed with a generalization of an error estimator originally derived for the Poisson equation. Our implementation of this algorithm is based on the widely used Open Source adaptive finite element library deal.II and is made available as part of this library’s extensively documented tutorial. We illustrate our methods with results for 2D and 3D reactor simulations using 2 and 7 energy groups, and using finite elements of polynomial degree up to 6. Key words: Finite elements, adaptive mesh refinement, multigroup diffusion approximation, reactor simulation. 1
1 An efficient numerical method for general Lp regularization in Fluorescence Molecular Tomography JeanCharles Baritaux † , Student Member, IEEE
"... Abstract—Reconstruction algorithms for fluorescence tomography have to address two crucial issues: (i) the illposedness of the reconstruction problem, (ii) the large scale of numerical problems arising from imaging of three dimensional samples. Our contribution is the design and implementation of a ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Abstract—Reconstruction algorithms for fluorescence tomography have to address two crucial issues: (i) the illposedness of the reconstruction problem, (ii) the large scale of numerical problems arising from imaging of three dimensional samples. Our contribution is the design and implementation of a reconstruction algorithm that incorporates general Lp regularization (p � 1). The originality of this work lies in the application of general constraints to fluorescence tomography, combined with an Lp efficient matrixfree strategy that enables the algorithm to deal with large reconstruction problems at reduced memory and computational costs. In the experimental part, we specialize the application of the algorithm to the case of sparsity promoting constraints (L1). We validate the adequacy of L1 regularization for the investigation of phenomena that are well described by a sparse model, using data acquired during phantom experiments. 1 I.
An Efficient Numerical Method for General Regularization in Fluorescence Molecular Tomography
"... Abstract—Reconstruction algorithms for fluorescence tomography have to address two crucial issues: 1) the illposedness of the reconstruction problem, 2) the large scale of numerical problems arising from imaging of 3D samples. Our contribution is the design and implementation of a reconstruction a ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract—Reconstruction algorithms for fluorescence tomography have to address two crucial issues: 1) the illposedness of the reconstruction problem, 2) the large scale of numerical problems arising from imaging of 3D samples. Our contribution is the design and implementation of a reconstruction algorithm that incorporates general regularization. The originality of this work lies in the application of general constraints to fluorescence tomography, combined with an efficient matrixfree strategy that enables the algorithm to deal with large reconstruction problems at reduced memory and computational costs. In the experimental part, we specialize the application of the algorithm to the case of sparsity promoting constraints. We validate the adequacy of regularization for the investigation of phenomena that are well described by a sparse model, using data acquired during phantom experiments. Index Terms—Fluorescence, image reconstruction, optical tomography. I.
4. TITLE AND SUBTITLE Model Variational Inverse Problems Governed by Partial Differential Equations
, 2011
"... Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments ..."
Abstract
 Add to MetaCart
(Show Context)
Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 222024302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.
unknown title
"... FaIMS: A fast algorithm for the inverse medium problem with multiple frequencies and multiple sources for the scalar Helmholtz equation ..."
Abstract
 Add to MetaCart
(Show Context)
FaIMS: A fast algorithm for the inverse medium problem with multiple frequencies and multiple sources for the scalar Helmholtz equation
FaIMS: A
, 2012
"... fast algorithm for the inverse medium problem with multiple frequencies and multiple sources for the scalar Helmholtz equation ..."
Abstract
 Add to MetaCart
(Show Context)
fast algorithm for the inverse medium problem with multiple frequencies and multiple sources for the scalar Helmholtz equation