Dispersion reducing methods for edge discretizations of the electric vector wave equation

We present a novel strategy for minimizing the numerical dispersion error in edge discretizations of the time-domain electric vector wave equation on square meshes based on the mimetic finite difference (MFD) method. We compare this strategy, called M-adaptation, to two other discretizations, also based on square meshes. One is the lowest order Nédélec edge element discretization. The other is a modified quadrature approach (GY-adaptation) proposed by Guddati and Yue for the acoustic wave equation in two dimensions. All three discrete methods use the same edge-based degrees of freedom, while the temporal discretization is performed using the standard explicit Leapfrog scheme. To obtain efficient and explicit time stepping methods, the three schemes are further mass lumped. We perform a dispersion and stability analysis for the presented schemes and compare all three methods in terms of their stability regions and phase error. Our results indicate that the method produced by GY-adaptation and the Nédélec method are both second order accurate for numerical dispersion, but differ in the order of their numerical anisotropy (fourth order, versus second order, respectively). The result of M-adaptation is a discretization that is fourth order accurate for numerical dispersion as well as numerical anisotropy. Numerical simulations are provided that illustrate the theoretical results.Keywords: Nédélec edge elements, Vector wave equation, M-adaptation, Maxwell’s equations, Anisotropy, Dispersio

Mimetic finite difference method for the stokes problem on polygonal meshes

Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure

ВПЛИВ НОВІТНІХ ІНТЕРАКТИВНИХ ТЕХНОЛОГІЙ НА БЕЗПЕРЕРВНИЙ ПРОФЕСІЙНИЙ РОЗВИТОК ЛІКАРІВ

The aim of the work – to reveal the structure and role of the educational and training center on 3D visualization in application of the latest interactive technologies with the continuous professional improvement of doctors and further development of the Kharkiv Medical Academy of Postgraduate Education (KhMAPE). The main body. The article presents the results of the implementation of a competence-oriented approach in postgraduate medical education with the introduction of educational interactive technologies, new forms and methods of organization of educational process. The role of the Training Center for 3D visualization technologies in the Kharkiv Medical Academy of Postgraduate Education (KhMAPE) has been revealed to ensure the quality of the educational process in accordance with the standards of higher education, normative documents on the organization of educational activities and policies in the field of quality education. Conclusion. When introducing the latest innovative technologies into the educational process, a higher percentage of mastering the material is noted during the use of the 3D visualization table, in addition, it indicates the higher progress of the knowledge gained by the students when using interactive technologies.Мета роботи – розкрити структуру та роль навчально-тренінгового центру з 3D-візуалізації у застосуванні новітніх інтерактивних технологій при безперервному професійному вдосконаленні лікарів та подальшому розвитку Харківської медичної академії післядипломної освіти. Основна частина. У статті наведено результати реалізації компетентнісно-орієнтованого підходу в післядипломній медичній освіті з впровадженням освітніх інтерактивних технологій, нових форм та методів організації навчального процесу. Розкрито роль навчально-тренінгового центру технологій 3D-візуалізацій у Харківській медичній академії післядипломної освіти для забезпечення якості освітнього процесу відповідно до стандартів вищої освіти, нормативних документів з організації освітньої діяльності та політики у сфері якості освіти. Висновок. При впровадженні  новітніх інноваційних технологій у навчальний процес відмічено більший відсоток засвоєння матеріалу при використанні 3D-візуалізаційного столу, крім цього, зазначено вищий прогрес отриманих знань слухачами при використанні інтерактивних технологій

LA-UR-(Y1~(J{J'763 Title: I MIMETIC FINITE DIFFERENCE METHOD FOR THE STOKES PROBLEM ON POLYGONAL MESHES t-; Mimetic finite difference method for the Stokes problem on polygonal meshes

Abstract Various approaches to extend the finite element methods to non-traditional elements pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry anal ysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex el ements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure

Hyperthermic intraperitoneal chemotherapy (HIPEC) in combined treatment of locally advanced and intraperitonealy disseminated gastric cancer: A retrospective cooperative Central-Eastern European study

Background and Objectives: Clinical experience in Western Europe suggests that cytoreductive surgery (CRS) and hyperthermic intraperitoneal chemotherapy (HIPEC) are promising methods in the management of gastric cancer (GC) with peritoneal metastases. However, there are almost no data on such treatment results in patient from Central‐Eastern European population. Methods: A retrospective cooperative study was performed at 6 Central‐Eastern European HIPEC centers. HIPEC was used in 117 patients for the following indications: treatment of GC with limited overt peritoneal metastases (n = 70), adjuvant setting after radical gastrectomy (n = 37) and palliative approach for elimination of severe ascites without gastrectomy (n = 10). Results: Postoperative morbidity and mortality rates were 29.1% and 5.1%, respectively. Median overall survival in the groups with therapeutic, adjuvant, and palliative indications was 12.6, 34, and 3.5 months. The only long‐term survivors occurred in the group with peritoneal cancer index (PCI) of 0‐6 points without survival difference in groups with PCI 7‐12 vs PCI 13 or more points. Conclusions: GC patients with limited peritoneal metastases can benefit from CRS + HIPEC. Hyperthermic intraperitoneal chemotherapy could be an effective method of adjuvant treatment of GC with a high risk of intraperitoneal progression. No long‐term survival may be expected after palliative approach to HIPEC