Communications in Numerical Methods in Engineering 

About: Communications in Numerical Methods in Engineering is an academic journal. The journal publishes majorly in the area(s): Finite element method & Numerical analysis. It has an ISSN identifier of 1069-8299. Over the lifetime, 1483 publications have been published receiving 24460 citations.

Near infrared optical tomography using nirfast: algorithm for numerical model and image reconstruction

Abstract: Diffuse optical tomography, also known as near infrared tomography, has been under investigation, for non-invasive functional imaging of tissue, specifically for the detection and characterization of breast cancer or other soft tissue lesions. Much work has been carried out for accurate modeling and image reconstruction from clinical data. NIRFAST, a modeling and image reconstruction package has been developed, which is capable of single wavelength and multi-wavelength optical or functional imaging from measured data. The theory behind the modeling techniques as well as the image reconstruction algorithms is presented here, and 2D and 3D examples are presented to demonstrate its capabilities. The results show that 3D modeling can be combined with measured data from multiple wavelengths to reconstruct chromophore concentrations within the tissue. Additionally it is possible to recover scattering spectra, resulting from the dominant Mie-type scatter present in tissue. Overall, this paper gives a comprehensive over view of the modeling techniques used in diffuse optical tomographic imaging, in the context of NIRFAST software package.

Balancing domain decomposition

Abstract: The Neumann–Neumann algorithm is known to be an efficient domain decomposition preconditioner with unstructured subdomains for iterative solution of finite-element discretizations of difficult problems with strongly discontinuous coefficients (De Roeck and Le Tallec, 1991). However, this algorithm suffers from the need to solve in each iteration an inconsistent singular problem for every subdomain, and its convergence deteriorates with increasing number of subdomains due to the lack of a coarse problem to propagate the error globally. We show that the equilibrium conditions for the singular problems on subdomains lead to a simple and natural construction of a coarse problem. The construction is purely algebraic and applies also to systems such as those that arise in elasticity. A convergence bound independent of the number of subdomains is proved and results of computational tests are reported.

Neural-network-based approximations for solving partial differential equations

Abstract: A numerical method, based on neural-network-based functions, for solving partial differential equations is reported in the paper. Using a ‘universal approximator’ based on a neural network and point collocation, the numerical problem of solving the partial differential equation is transformed to an unconstrained minimization problem. The method is extremely easy to implement and is suitable for obtaining an approximate solution in a short period of time. The technique is illustrated with the aid of two numerical examples.

Total Lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation

Abstract: We propose an efficient numerical algorithm for computing deformations of ‘very’ soft tissues (such as the brain, liver, kidney etc.), with applications to real-time surgical simulation. The algorithm is based on the finite element method using the total Lagrangian formulation, where stresses and strains are measured with respect to the original configuration. This choice allows for pre-computing of most spatial derivatives before the commencement of the time-stepping procedure. We used explicit time integration that eliminated the need for iterative equation solving during the time-stepping procedure. The algorithm is capable of handling both geometric and material non-linearities. The total Lagrangian explicit dynamics (TLED) algorithm using eight-noded hexahedral under-integrated elements requires approximately 35% fewer floating-point operations per element, per time step than the updated Lagrangian explicit algorithm using the same elements. Stability analysis of the algorithm suggests that due to much lower stiffness of very soft tissues than that of typical engineering materials, integration time steps a few orders of magnitude larger than what is typically used in engineering simulations are possible. Numerical examples confirm the accuracy and efficiency of the proposed TLED algorithm. Copyright © 2006 John Wiley & Sons, Ltd.

A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications

Abstract: This paper presents a simple linear tetrahedron element that can be used in explicit dynamics applications involving nearly incompressible materials or incompressible materials modelled using a penalty formulation. The element prevents volumetric locking by defining nodal volumes and evaluating average nodal pressures in terms of these volumes. Two well-known examples relating to the impact of elasto–plastic bars are used to demonstrate the ability of the element to model large isochoric strains without locking. © 1998 John Wiley & Sons, Ltd.