Experimental validation of a three-dimensional linear system model for breast tomosynthesis

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

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An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

Volume 1: Heat Transfer in Energy Systems; Thermophysical Properties; Heat Transfer Equipment; Heat Transfer in Electronic Equipment ◽

10.1115/ht2009-88140 ◽

2009 ◽

Author(s):

Gisela Widmer

Keyword(s):

Linear System ◽

Radiative Transfer ◽

Transfer Equation ◽

Degrees Of Freedom ◽

Radiative Transfer Equation ◽

Three Dimensional ◽

Discrete Ordinates ◽

Five Dimensions ◽

Computational Costs ◽

Dimensional Domain

The stationary monochromatic radiative transfer equation (RTE) is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For non-scattering radiative transfer, sparse finite elements [1, 2] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared to the discrete ordinates method, they make it possible to significantly reduce the number of degrees of freedom N in the discretization with almost no loss of accuracy. However, using a direct solver to solve the resulting linear system requires O(N3) operations. In this paper, an efficient solver based on the conjugate gradient method (CG) with a subspace correction preconditioner is presented. Numerical experiments show that the linear system can be solved at computational costs that are nearly proportional to the number of degrees of freedom N in the discretization.

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A novel damage indicator from a multivariate linear system model

Life-Cycle of Engineering Systems ◽

10.1201/9781315375175-86 ◽

2016 ◽

pp. 705-712

Author(s):

Y. Goi ◽

C.W. Kim

Keyword(s):

Linear System ◽

System Model ◽

Damage Indicator

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An Evaluation and Implementation of the Regional Coupled Ice-Ocean Model of the Baltic Sea

10.5194/esd-2017-35 ◽

2017 ◽

Author(s):

Jaromir Jakacki ◽

Sebastian Meler

Keyword(s):

Baltic Sea ◽

Three Dimensional ◽

Coupled Model ◽

Horizontal Resolution ◽

Ocean Model ◽

System Model ◽

The Baltic Sea ◽

Community Earth System Model ◽

The Baltic ◽

Ice Model

Abstract. A three dimensional, regional coupled ice-ocean model based on the open-source Community Earth System Model has been developed and implemented for the Baltic Sea. The model consists of 66 vertical levels and has a horizontal resolution of approx. 2.3 km. The paper focuses on sea ice component results but the main changes have been introduced in the ocean part of the coupled model. The hydrodynamic part, being one of the most important components, has been also presented and validated. The ice model results were validated against the radar and satellite data, and the method of validation based on probability was introduced. In the last two decades satellite and model results show an increase in the ice extent over the whole Baltic Sea, which is an evidence of a negative trend in air temperature in recent decades and increasing of winter discharge from the catchment area.

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Tecnica di Imaging tridimensionale (Digital Breast Tomosynthesis) per la diagnosi del tumore alla mammella

Journal of Advanced Health Care ◽

10.36017/jahc1908-007 ◽

2019 ◽

Author(s):

Di Guida Lisa ◽

De Rosa Salvatore

Keyword(s):

Breast Cancer ◽

Early Diagnosis ◽

Imaging Techniques ◽

Three Dimensional ◽

Digital Breast Tomosynthesis ◽

Recurrence Time ◽

Digital Tomosynthesis ◽

Breast Tomosynthesis ◽

X Ray Imaging ◽

Projective Image

Breast cancer affects one in eight women over a lifetime. It is the most common cancer in women and represents 29% of all cancers affecting women, with a mortality rate of 17% of all deaths due to cancer on women. Sooner the cancer is identified with an early diagnosis, higher are the possibilities to treat it completely and longer is the recurrence time. Mammography is the most common method for early diagnosis. is a two-dimensional X-ray imaging technique and this involves the overlapping of the tissues in the projective image inability to visualize cancer in the first stage. In recent years, three-dimensional imaging techniques have been introduced, including digital tomosynthesis for the diagnosis of breast cancer, this technique has the advantages to perform dozens of projections, and not just one, from various angular views around the compressed breast. The major benefits of tomosynthesis are a lower stratification of breast tissues, better visibility of tumor masses especially for small tumors, breast tomosynthesis provides the ability to visualize 3D images to obtain a more accurated evaluation of lesions allowing better differentiation between overlapping fabrics.

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