A Priori Subcell Limiting Approach for the FR/CPR Method on Unstructured Meshes

A priori subcell limiting approach is developed for high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) methods on two-dimensional unstructured quadrilateral meshes. Firstly, a modified indicator based on modal energy coefficients is proposed to detect troubled cells, where discontinuities exist. Then, troubled cells are decomposed into nonuniform subcells and each subcell has one solution point. A second-order finite difference shock-capturing scheme based on nonuniform nonlinear weighted (NNW) interpolation is constructed to perform the calculation on troubled cells while smooth cells are calculated by the CPR method. Numerical investigations show that the proposed subcell limiting strategy on unstructured quadrilateral meshes is robust in shock-capturing.     

An Adaptive Threshold Dynamics Method for Three-Dimensional Wetting on Rough Surfaces

We propose an adaptive threshold dynamics method for wetting problems in three space dimensions. The method is based on solving a linear heat equation and a thresholding step in each iteration. The heat equation is discretized by a cell-centered finite volume method on an adaptively refined mesh. An efficient technique for volume conservation is developed on the nonuniform meshes based on a quick-sorting operation. By this method, we compute some interesting wetting problems on complicated surfaces. Numerical results verify some recent theories for the apparent contact angle on rough and chemically patterned surfaces.     

Biological behavior of polypropylene meshes suitable for intra-abdominal implantation in animal model

The expected incisional hernia rate is between 11-20% after laparotomy. Using mesh repair the results of the hernioplasty have recently improved. However the complication of mesh implants--especially in intraperitoneal position--can be life threatening. Additionally the appropriate mesh is expensive. We tried to create a mesh, which can be used intraperitoneally and generates adhesion in the abdominal wall, but keeps the intraabdominal organs adhesion free. Our experiments were divided into four groups. In the first we used different materials to cover the intraperitoneal side of polypropylene mesh. In the second phase three different pore-sized meshes were compared. In the third part the biological behavior of three different material-reduced meshes were investigated. Based on our previous results in the last session we used only silicone membrane protected material-reduced polypropylene meshes to cover the abdominal defects. Our experiments have shown that intraperitoneal implant with silicone-covered Vypro (Ethicon)/Premilene (B. Braun Medical) mesh significantly decreases the formations of adhesion.     

Numerical Methods for Balance Laws with Space Dependent Flux: Application to Radiotherapy Dose Calculation

The present work is concerned with the derivation of numerical methods to approximate the radiation dose in external beam radiotherapy. To address this issue, we consider a moment approximation of radiative transfer, closed by an entropy minimization principle. The model under consideration is governed by a system of hyperbolic equations in conservation form supplemented by source terms. The main difficulty coming from the numerical approximation of this system is an explicit space dependence in the flux function. Indeed, this dependence will be seen to be stiff and specific numerical strategies must be derived in order to obtain the needed accuracy. A first approach is developed considering the 1D case, where a judicious change of variables allows to eliminate the space dependence in the flux function. This is not possible in multi-D. We therefore reinterpret the 1D scheme as a scheme on two meshes, and generalize this to 2D by alternating transformations between separate meshes. We call this procedure projection method. Several numerical experiments, coming from medical physics, illustrate the potential applicability of the developed method.     

An Adaptive Moving Mesh Method for Two-Dimensional Relativistic Hydrodynamics

This paper extends the adaptive moving mesh method developed by Tang and Tang [36] to two-dimensional (2D) relativistic hydrodynamic (RHD) equations. The algorithm consists of two "independent" parts: the time evolution of the RHD equations and the (static) mesh iteration redistribution. In the first part, the RHD equations are discretized by using a high resolution finite volume scheme on the fixed but nonuniform meshes without the full characteristic decomposition of the governing equations. The second part is an iterative procedure. In each iteration, the mesh points are first redistributed, and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative way. Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.     

Comparison of a lightweight polypropylene mesh (Optilene® LP) and a large-pore knitted PTFE mesh (GORE® INFINIT® mesh)—Biocompatibility in a standardized endoscopic extraperitoneal hernia model

Purpose  

The use of a mesh with good biocompatibility properties is of decisive importance for the avoidance of recurrences and chronic pain in endoscopic hernia repair surgery. As we know from numerous experiments and clinical experience, large-pore, lightweight polypropylene meshes possess the best biocompatibility. However, large-pore meshes of different polymers may be used as well and might be an alternative solution.     

Experimental comparison of type of Tissucol dilution and composite mesh (Parietex) for laparoscopic repair of groin and abdominal hernia: observational study conducted in a university laboratory

Purpose The primary objective of this observational study was to determine the best possible dilution of fibrin glue (Tissucol) to employ for prosthesis fixing in laparoscopic treatment of abdominal wall defects and, secondly, to assess its feasibility and safety. Materials and methods This study was carried out in a university experimental animal laboratory in accordance with all international laws, ethics regulations and quality criteria associated with animal experiments. The tests were carried out on two pigs, using four samples of mesh (Parietex). All meshes were fixed using two different Tissucol dilutions (standard with distilled water and that with calcium chloride). Follow-up evaluations were at 15 days after 30 days, with the latter consisting of traction tests and a biopsy for histological analysis. Results No post-operative complications were observed. The collagen-coated polyester meshes showed 0% adhesions, and reperitonealization had ensued after 15 days. We saw no shrinkage or migration of any of the meshes. Histopathological analyses confirmed a greater stability, greater tissue integration and the largest number of fibroblasts in meshes fixed with a 1/10 Tissucol dilution without calcium chloride. Conclusions This observational study using animals showed that the 1/10 standard dilution – not that with calcium chloride – provided the best fixation and integration and prevented the formation of intraperitoneal adhesions, provided a hydrophilic collagen film-covered mesh was used.     

Discrete Duality Finite Volume Discretization of the Thermal-$P_N$ Radiative Transfer Equations on General Meshes

The discrete duality finite volume method has proven to be a practical tool for discretizing partial differential equations coming from a wide variety of areas of physics on nearly arbitrary meshes. The main ingredients of the method are: (1) use of three meshes, (2) use of the Gauss-Green theorem for the approximation of derivatives, (3) discrete integration by parts. In this article we propose to extend this method to the coupled grey thermal-$P_N$ radiative transfer equations in Cartesian and cylindrical coordinates in order to be able to deal with two-dimensional Lagrangian approximations of the interaction of matter with radiation. The stability under a Courant-Friedrichs-Lewy condition and the preservation of the diffusion asymptotic limit are proved while the experimental second-order accuracy is observed with manufactured solutions. Several numerical experiments are reported which show the good behavior of the method.     

A Continuous Finite Element Method with Homotopy Vanishing Viscosity for Solving the Static Eikonal Equation

We develop a second-order continuous finite element method for solving the static Eikonal equation. It is based on the vanishing viscosity approach with a homotopy method for solving the discretized nonlinear system. More specifically, the homotopy method is utilized to decrease the viscosity coefficient gradually, while Newton’s method is applied to compute the solution for each viscosity coefficient. Newton’s method alone converges for just big enough viscosity coefficients on very coarse grids and for simple 1D examples, but the proposed method is much more robust and guarantees the convergence of the nonlinear solver for all viscosity coefficients and for all examples over all grids. Numerical experiments from 1D to 3D are presented to confirm the second-order convergence and the effectiveness of the proposed method on both structured or unstructured meshes.     

An LDG Method for Stochastic Cahn-Hilliard Type Equation Driven by General Multiplicative Noise Involving Second-Order Derivative

In this paper, we propose a local discontinuous Galerkin (LDG) method for the multi-dimensional stochastic Cahn-Hilliard type equation in a general form, which involves second-order derivative $∆u$ in the multiplicative noise. The stability of our scheme is proved for arbitrary polygonal domain with triangular meshes. We get the sub-optimal error estimate $\mathbb{O}(h^k)$ if the Cartesian meshes with $Q^k$ elements are used. Numerical examples are given to display the performance of the LDG method.     

Comparison of outcomes of ventral hernia repair using different meshes: a systematic review and network meta-analysis

Hernia - We conducted a network meta-analysis to evaluate potential differences in patient outcomes when different meshes, especially biological meshes, were used for ventral hernia repair. PubMed,...     

Adaptive hp-Finite Element Computations for Time-Harmonic Maxwell's Equations

In this paper, hp-adaptive finite element methods are studied for time-harmonic Maxwell's equations. We propose the parallel hp-adaptive algorithms on conforming unstructured tetrahedral meshes based on residual-based a posteriori error estimates. Extensive numerical experiments are reported to investigate the efficiency of the hp-adaptive methods for point singularities, edge singularities, and an engineering benchmark problem of Maxwell's equations. The hp-adaptive methods show much better performance than the h-adaptive method.     

Abdominal vascular injuries: Blunt vs. penetrating

Introduction: Abdominal vascular injuries (AVIs) remain a great challenge since they are associated with significant mortality. Penetrating injury is the most common cause of AVIs; however, some AVI series had more blunt injuries. There is little information regarding differences between penetrating and blunt AVIs. The objective of the present study was to identify the differences between these two mechanisms in civilian AVI patients in terms of patient’s characteristics, injury details, and outcomes.Method: From January 2007 to January 2016, we retrospectively collected the data of AVI patients at King Chulalongkorn Memorial hospital, including demographic data, details of injury, the operative managements, and outcomes in terms of morbidity and mortality. The comparison of the data between blunt and penetrating AVI patients was performed.Results: There were 55 AVI patients (28 blunt and 27 penetrating). Majority (78%) of the patients in both groups were in shock on arrival. Blunt AVI patients had significantly higher injury severity score (mean(SD) ISS, 36(20) vs. 25(9), p?=?0.019) and more internal iliac artery injuries (8 vs. 1, p?=?0.028). On the other hand, penetrating AVI patients had more aortic injuries (5 vs. 0, p?=?0.046), and inferior vena cava injuries (7 vs. 0, p?=?0.009). Damage control surgery (DCS) was performed in 45 patients (82%), 25 in blunt and 20 in penetrating. The overall mortality rate was 40% (50% in blunt vs. 30% in penetrating, p?=?0.205).Conclusions: Blunt AVI patients had higher ISS and more internal iliac artery injuries, while penetrating AVI patients had more aortic injuries and vena cava injuries. Majority of AVI patients in both groups presented with shock and required DCS.     

On Triangular Lattice Boltzmann Schemes for Scalar Problems

We propose to extend the d'Humières version of the lattice Boltzmann scheme to triangular meshes. We use Bravais lattices or more general lattices with the property that the degree of each internal vertex is supposed to be constant. On such meshes, it is possible to define the lattice Boltzmann scheme as a discrete particle method, without need of finite volume formulation or Delaunay-Voronoi hypothesis for the lattice. We test this idea for the heat equation and perform an asymptotic analysis with the Taylor expansion method for two schemes named D2T4 and D2T7. The results show a convergence up to second order accuracy and set new questions concerning a possible super-convergence.     

Anisotropic evaluation of synthetic surgical meshes

Introduction  

The material properties of meshes used in hernia repair contribute to the overall mechanical behavior of the repair. The anisotropic potential of synthetic meshes, representing a difference in material properties (e.g., elasticity) in different material axes, is not well defined to date. Haphazard orientation of anisotropic mesh material can contribute to inconsistent surgical outcomes. We aimed to characterize and compare anisotropic properties of commonly used synthetic meshes.     

An Efficient Positivity-Preserving Finite Volume Scheme for the Nonequilibrium Three-Temperature Radiation Diffusion Equations on Polygonal Meshes

This paper develops an efficient positivity-preserving finite volume scheme for the two-dimensional nonequilibrium three-temperature radiation diffusion equations on general polygonal meshes. The scheme is formed as a predictor-corrector algorithm. The corrector phase obtains the cell-centered solutions on the primary mesh, while the predictor phase determines the cell-vertex solutions on the dual mesh independently. Moreover, the flux on the primary edge is approximated with a fixed stencil and the nonnegative cell-vertex solutions are not reconstructed. Theoretically, our scheme does not require any nonlinear iteration for the linear problems, and can call the fast nonlinear solver (e.g. Newton method) for the nonlinear problems. The positivity, existence and uniqueness of the cell-centered solutions obtained on the corrector phase are analyzed, and the scheme on quasi-uniform meshes is proved to be $L^2$- and $H^1$-stable under some assumptions. Numerical experiments demonstrate the accuracy, efficiency and positivity of the scheme on various distorted meshes.     

Modeling Ionic Polymer-Metal Composites with Space-Time Adaptive Multimesh hp-FEM

We are concerned with a model of ionic polymer-metal composite (IPMC) materials that consists of a coupled system of the Poisson and Nernst-Planck equations, discretized by means of the finite element method (FEM). We show that due to the transient character of the problem it is efficient to use adaptive algorithms that are capable of changing the mesh dynamically in time. We also show that due to large qualitative and quantitative differences between the two solution components, it is efficient to approximate them on different meshes using a novel adaptive multimesh hp-FEM. The study is accompanied with numerous computations and comparisons of the adaptive multimesh hp-FEM with several other adaptive FEM algorithms.     

A Finite Volume Upwind-Biased Centred Scheme for Hyperbolic Systems of Conservation Laws: Application to Shallow Water Equations

We construct a new first-order central-upwind numerical method for solving systems of hyperbolic equations in conservative form. It applies in multidimensional structured and unstructured meshes. The proposed method is an extension of the UFORCE method developed by Stecca, Siviglia and Toro [25], in which the upwind bias for the modification of the staggered mesh is evaluated taking into account the smallest and largest wave of the entire Riemann fan. The proposed first-order method is shown to be identical to the Godunov upwind method in applications to a 2×2 linear hyperbolic system. The method is then extended to non-linear systems and its performance is assessed by solving the two-dimensional inviscid shallow water equations. Extension to second-order accuracy is carried out using an ADER-WENO approach in the finite volume framework on unstructured meshes. Finally, numerical comparison with current competing numerical methods enables us to identify the salient features of the proposed method.     

A Decoupled and Positivity-Preserving DDFVS Scheme for Diffusion Problems on Polyhedral Meshes

We propose a decoupled and positivity-preserving discrete duality finite volume (DDFV) scheme for anisotropic diffusion problems on polyhedral meshes with star-shaped cells and planar faces. Under the generalized DDFV framework, two sets of finite volume (FV) equations are respectively constructed on the dual and primary meshes, where the ones on the dual mesh are derived from the ingenious combination of a geometric relationship with the construction of the cell matrix. The resulting system on the dual mesh is symmetric and positive definite, while the one on the primary mesh possesses an M-matrix structure. To guarantee the positivity of the two categories of unknowns, a cutoff technique is introduced. As for the local conservation, it is conditionally maintained on the dual mesh while strictly preserved on the primary mesh. More interesting is that the FV equations on the dual mesh can be solved independently, so that the two sets of FV equations are decoupled. As a result, no nonlinear iteration is required for linear problems and a general nonlinear solver could be used for nonlinear problems. In addition, we analyze the well-posedness of numerical solutions for linear problems. The properties of the presented scheme are examined by numerical experiments. The efficiency of the Newton method is also demonstrated by comparison with those of the fixed-point iteration method and its Anderson acceleration.     

腹壁切口疝复发因素及应对策略

腹壁切口疝是外科手术后严重并发症,切口疝复发也是国内外疝外科医师的关注焦点之一。其复发受到多因素的影响,如患者因素、修补方式及补片等。如何降低复发率是当今国内外领域一直探讨的问题,补片无张力修补已成为复发切口疝的主要治疗手段之一,针对不同复发切口疝选择合适的修补材料,同时联合一些新技术,如成分分离技术（component separation technique,CST）,"三明治"技术（Sandwich technique）能够获得理想的长期修补效果。