Search results for "Numerical Analysis"
showing 10 items of 883 documents
Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation
2020
We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp., 69:481-500, 2000] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computa…
Optimal recovery of a radiating source with multiple frequencies along one line
2020
We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If measurements are carried out with frequencies ranging in an open set, we show that the source density is uniquely determined by these measurements up to averaging over levelsets of the integrated attenuation. This leads to a generalized Laplace transform. We also discuss some numerical approaches and demonstrate the results with several examples.
A simulation function approach for best proximity point and variational inequality problems
2017
We study sufficient conditions for existence of solutions to the global optimization problem min(x is an element of A) d(x, fx), where A, B are nonempty subsets of a metric space (X, d) and f : A -> B belongs to the class of proximal simulative contraction mappings. Our results unify, improve and generalize various comparable results in the existing literature on this topic. As an application of the obtained theorems, we give some solvability theorems of a variational inequality problem.
Precise and efficient parametric path analysis
2012
Hard real-time systems require tasks to finish in time. To guarantee the timeliness of such a system, static timing analyses derive upper bounds on the worst-case execution time (WCET) of tasks. There are two types of timing analyses: numeric and parametric. A numeric analysis derives a numeric timing bound and, to this end, assumes all information such as loop bounds to be given a priori. If these bounds are unknown during analysis time, a parametric analysis can compute a timing formula parametric in these variables. A performance bottleneck of timing analyses, numeric and especially parametric, is the so-called path analysis, which determines the path in the analyzed task with the longes…
Shakedown of elastic—plastic solids with frictionless unilateral contact boundary conditions
1997
Abstract Elastic perfectly plastic solids (or structures) in frictionless unilateral contact with a rigid obstacle and subjected to quasi-statically variable loads within a given domain are considered. In the hypothesis that the structure undergoes small displacements and complies with a d -stability requisite herein introduced, a Melantype shakedown theorem is presented. This theorem is conceptually similar to the classical one; namely, it requires that the unilateral-contact elastic stress response to the loads and to some initial plastic strains be plastically admissible everywhere in the body and for all load conditions. A method for evaluating the shakedown load boundary is also discus…
Accuracy of stereotactic coordinate transformation using a localisation frame and computed tomographic imaging
1999
The accuracy of coordinate transformation from a CT image to a stereotactic frame was investigated for stereotactic systems using a localisation frame and matrix-based coordinate transformation. The main source of error influencing calculation was input data, due to inaccurate calculation of the centres of the rods of the localisation frame in the CT image, and the propagation of this input error during subsequent matrix calculation. Systemic errors during matrix calculation do not exist, and rounding off errors were of subordinate importance compared to the input data error. The influence of input data error on coordinate transformation was studied by geometric methods, computer simulation…
Computer-Aided Simulation of Die Filling Processes
1989
Summary A numerical method for analysing the filling of axisymmetrical dies of complex shape is proposed. The method, which is a further development of a LP finite element model, is able to take into account the contact conditions directly in the mathematical formulation of the problem. In such a way the solution of the die filling process is obtained by solving a LP problem, avoiding problems of numerical convergence and the heavier calculations requested by other iterative methods.
Experimental Investigations and Numerical Analysis for Improving Knowledge of Incremental Sheet Forming Process for Sheet Metal Parts
2009
The paper is related to the analysis of shape distortions and springback effects arising in Single Point Incremental Forming. An experimental set up has been designed and manufactured to carry single point incremental forming on small size sheet metal parts. The experimental set up is mounted on 3-axes CNC milling machine tool and the forming tool is attached and move with the spindle. Experiments have been carried out on sheet metal parts to obtain tronconical shapes. The forming strategy associated to the movement of the forming tool has been also investigated. The experiments indicate that shape distortions arising in the corners of the tronconical shape are clearly related to forming st…
A Qualitative-Quantitative Approach to V-Belt Mechanics
1996
A simplified formulation is adopted for the theoretical problem of tension distribution and radial penetration of a V-belt along the pulley groove. The trajectory portrait of the second order differential system describing the belt behavior is carefully analyzed and asymptotic approximations for the tension solutions are derived which are well suited for design purposes.
Experimental analysis of "bovedas tabicadas"
2012
A particular type of vaulted structures, known as bóvedas tabicadas (Catalan vaults), made with alternate layers of bricks and mortar and characterized by a very low thickness in comparison to the other two dimensions, are studied. The research has been faced under the historical aspect as well as under the mechanical one, developing experimental and numerical analysis regarding real existing structures. In particular, the experimental analysis, performed by effecting compression and bending tests on samples taken from a real structure, has been devoted to the constitutive material identification and the characterization is made by considering the material as an ideal homogeneous; further e…