A P1 -nonconforming quadrilateral finite element is introduced for second-order elliptic problems in two dimensions. Unlike the usual nonconforming elements, which contain quadratic polynomials or of degree greater than 2, our consists only piecewise linear that are continuous at midpoints edges. One benefits using convenience rectangular meshes with least degrees freedom among elements. An optimal rate convergence obtained. Also a nonparametric reference scheme order to systematically...

In magnetic resonance electrical impedance tomography (MREIT), we measure the induced flux density inside an object subject to externally injected current. This is contaminated with noise, which ultimately limits quality of reconstructed conductivity and current images. By analysing experimentally verifying amount noise in images gathered from two MREIT systems, found that a carefully designed study will be able reduce levels below 0.25 0.05 nT at main field strengths 3 11 T, respectively,...

Magnetic resonance electrical impedance tomography (MREIT) aims at producing high-resolution cross-sectional conductivity images of an electrically conducting object such as the human body. Following numerous phantom imaging experiments, most recent study demonstrated successful image reconstructions postmortem canine brains using a 3 T MREIT system with 40 mA currents. Here, we report results in vivo animal experiments 5 To investigate any change due to brain ischemia, having regional...

Magnetic resonance current density imaging (MRCDI) provides a image by measuring the induced magnetic flux within subject with (MRI) scanner. electrical impedance tomography (MREIT) has been focused on extracting some useful information of and conductivity distribution in Omega using measured B(z), one component B. In this paper, we analyze map Tau from vector field J to B(z) without any assumption conductivity. The an orthogonal decomposition = J(P) + J(N) where belongs null space Tau. We...

Abstract The objective of the present study is to show that numerical instability characterized by checkerboard patterns can be completely controlled when non‐conforming four‐node finite elements are employed. Since convergence element independent Lamé parameters, stiffness exhibits correct limiting behaviour, which desirable in prohibiting unwanted formation checkerboards topology optimization. We employ homogenization method checkerboard‐free property optimization problems and verify it...

Magnetic resonance elastography (MRE) is an imaging modality capable of visualizing the elastic properties object using magnetic (MRI) measurements transverse acoustic strain waves induced in by a harmonically oscillating mechanical vibration. Various algorithms have been designed to determine under assumptions linear elasticity, isotropic and local homogeneity. One challenging problems MRE reduce noise effects maintain contrast reconstructed shear modulus images. In this paper, we propose...

Magnetic resonance electrical impedance tomography (MREIT) is designed to produce high resolution conductivity images of an electrically conducting subject by injecting current and measuring the longitudinal component, Bz, induced magnetic flux density B = (Bx, By, Bz). In MREIT, accurate measurements Bz are essential in producing correct images. However, measured data may contain fundamental defects local regions where MR magnitude image small. These defective result completely wrong values...

Magnetic resonance electrical impedance tomography (MREIT) is to visualize the current density and conductivity distribution in an object Omega using measured magnetic flux data by MRI scanner. MREIT uses only one component B(z) of B = (B(x), B(y), B(z)) generated injected into object. In this paper, we propose a fast direct non-iterative algorithm reconstruct internal with data. To develop algorithm, investigate relation between projected J(P), uniquely determined J map from isotropic...

An aim of magnetic resonance electrical impedance tomography (MREIT) is to visualize the internal current density and conductivity electrically imaged object by injecting through electrodes attached it. Due a limited amount injection current, one most important factors in MREIT how control noise contained measured flux data. This paper describes new iterative algorithm called transversal J-substitution which robust noise. As result, proposed considerably improves quality reconstructed image...

In magnetic resonance electrical impedance tomography (MREIT), we inject current into a volume conductor to induce distribution of flux density. By measuring the internal density using an MR scanner, reconstruct images cross-sectional conductivity and distributions. One most important technical problems in MREIT is reduce noise level measured data since it limits quality reconstructed images. The inversely proportional injection pulse width signal-to-noise ratio (SNR) magnitude Knowing that...

Magnetic resonance current density imaging (MRCDI) and magnetic electrical impedance tomography (MREIT) visualize an internal distribution of and/or conductivity by injecting into electrically conductive object such as the human body using MRI scanner. MREIT measures induced flux which appears in phase part acquired MR image data. Recently, injected nonlinear encoding (ICNE) method extended duration injection until end a reading gradient to maximize signal intensity density. In this paper,...

We introduce a piecewise P2-nonconforming quadrilateral finite element. First, we decompose convex into the union of four triangles divided by its diagonals. Then element space is defined set all P2-polynomials that are quadratic in each triangle and continuously differentiable on quadrilateral. The degrees freedom (DOFs) eight values at two Gauss points edges plus value intersection Due to existence one linear relation among above DOFs, it turns out DOFs eight. Global basis functions three...

We introduce a new stable MINI-element pair for incompressible Stokes equations on quadrilateral meshes, which uses the smallest number of bubbles velocity. The pressure is discretized with P1-midpoint-edge-continuous elements and each component velocity field done standard Q1-conforming enriched by one bubble quadrilateral. superconvergence in proposed analyzed uniform rectangular tested numerically non-uniform meshes.

Magnetic resonance electrical impedance tomography (MREIT) measures magnetic flux density signals through the use of a imaging (MRI) in order to visualize internal conductivity and/or current density. Understanding reconstruction procedure for density, we directly measure second derivative of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math>data from measured<mml:math...

Abstract This article will suggest a new finite element method to find ‐velocity and ‐pressure solving incompressible Stokes equations at low cost. The solves first the decoupled equation for ‐velocity. Then, using calculated velocity, locally calculable be defined component‐wisely. resulting is analyzed have optimal order of convergence. Since pressure by local computation only, chief time cost on Besides, overcomes problem singular vertices or corners.

Erikkson showed that singular value decomposition(SVD) of flattenings determined a partition phylogenetic tree to be split. In this paper, based on his work, we develop new statistically consistent algorithms fit for grid computing construct by SVD with the small fixed number rows.

Recently, the $P_1$-nonconforming finite element space over square meshes has been proved stable to solve Stokes equations with piecewise constant for velocity and pressure, respectively. In this paper, we will introduce its locally divergence-free subspace elliptic problem only decoupled from equation. The concerning system of linear is much smaller compared equations. Furthermore, it split into two ones. After solving first, pressure in can be obtained by an explicit method very rapidly.