A family of C-1 quadrilateral finite elements

We present a novel family of C-1 quadrilateral finite elements, which define global C-1 spaces over a general quadrilateral mesh with vertices of arbitrary valency. The elements extend the construction by Brenner and Sung (J. Sci. Comput. 22(1-3), 83-118, 2005), which is based on polynomial elements of tensor-product degree p >= 6, to all degrees p >= 3. The proposed C-1 quadrilateral is based upon the construction of multi-patch C-1 isogeometric spaces developed in Kapl et al. (Comput. Aided Geometr. Des. 69, 55-75 2019). The quadrilateral elements possess similar degrees of freedom as the classical Argyris triangles, developed in Argyris et al. (Aeronaut. J. 72(692), 701-709 1968). Just as for the Argyris triangle, we additionally impose C-2 continuity at the vertices. In contrast to Kapl et al. (Comput. Aided Geometr. Des. 69, 55-75 2019), in this paper, we concentrate on quadrilateral finite elements, which significantly simplifies the construction. We present macro-element constructions, extending the elements in Brenner and Sung (J. Sci. Comput. 22(1-3), 83-118 2005), for polynomial degrees p = 3 and p = 4 by employing a splitting into 3 x 3 or 2 x 2 polynomial pieces, respectively. We moreover provide approximation error bounds in L-infinity, L-2, H-1 and H-2 for the piecewise-polynomial macro-element constructions of degree p is an element of{3,4} and polynomial elements of degree p >= 5. Since the elements locally reproduce polynomials of total degree p, the approximation orders are optimal with respect to the mesh size. Note that the proposed construction combines the possibility for spline refinement (equivalent to a regular splitting of quadrilateral finite elements) as in Kapl et al. (Comput. Aided Geometr. Des. 69, 55-75 30) with the purely local description of the finite element space and basis as in Brenner and Sung (J. Sci. Comput. 22(1-3), 83-118 2005). In addition, we describe the construction of a simple, local basis and give for p is an element of{3,4,5} explicit formulas for the Bezier or B-spline coefficients of the basis functions. Numerical experiments by solving the biharmonic equation demonstrate the potential of the proposed C1 quadrilateral finite element for the numerical analysis of fourth order problems, also indicating that (for p = 5) the proposed element performs comparable or in general even better than the Argyris triangle with respect to the number of degrees of freedom

Manifold-Based B-Splines on Unstructured Meshes

We introduce new manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes. Such splines can be used in isogeometric analysis (IGA) to represent smooth surfaces of arbitrary topology. Since prevalent computer-aided design (CAD) models are composed of tensor-product B-spline patches, any IGA suitable construction should be able to reproduce B-splines. To achieve this goal, we focus on univariate manifold-based constructions that can reproduce B-splines. The manifold-based splines are constructed by smoothly blending together polynomial interpolants defined on overlapping charts. The proposed constructions automatically reproduce B-splines in regular parts of the mesh, with no extraordinary vertices, and polynomial basis functions in the remaining parts of the mesh. We study and compare analytically and numerically the finite element convergence of several univariate constructions. The obtained results directly carry over to the tensor-product case

Interrelated aldosterone and parathyroid hormone mutually modify cardiovascular mortality risk

BACKGROUND: Inappropriate aldosterone and parathyroid hormone (PTH) secretion is associated with increased cardiovascular risk. Accumulating evidence suggests bidirectional interplay between aldosterone and PTH. METHODS: We evaluated the cross-sectional relationship between plasma aldosterone concentration (PAC), aldosterone to renin ratio (ARR) and PTH and subsequently tested whether the interaction between PAC and PTH modified the risk of cardiovascular death. PAC [78.0 (48.0-123.0) pg/mL], ARR [6.4 (2.9-12.9) pg/mL/pg/mL] and PTH concentration [median: 29.0 (22.0-40.0) pg/mL] were measured in 3074 patients (mean age: 62.5 ± 10.6 years; 30.3% women) referred to coronary angiography in a tertiary care center in Southwest Germany. RESULTS: Using multiple linear regression analysis, PAC and ARR emerged as an independent predictor of higher PTH concentrations (β=0.12 and 0.21, P<0.001 for both) irrespective of intake of antihypertensive treatment, 25(OH)D, kidney function, serum calcium, phosphate, magnesium, cortisol, NT-pro-BNP, soluble α-klotho and FGF-23 concentration. After a median follow-up of 9.9 years, 512 (16.7%) participants had died due to fatal cardiovascular events. Multivariate Cox proportional hazard analysis revealed that both PAC and PTH were independently associated with cardiovascular mortality, with a potential synergistic interaction (P=0.028). PAC and PTH are exclusively associated with cardiovascular death in subjects with PTH and PAC concentrations above the median, respectively (PAC: HR per log SD: 1.14; 95% CI 1.02-1.29; P=0.026; PTH: HR per log SD: 1.18; 95% CI 1.02-1.37; P=0.031). CONCLUSIONS: Higher PAC and ARR were independently associated with PTH. PAC was independently related to incident cardiovascular mortality exclusively in patients with elevated PTH and vice versa

Warum können Patientinnen mit Anorexia nervosa depressiv und trotzdem leistungsfähig sein? Die mögliche Bedeutung von emotionaler Suppression im Rahmen eines leistungsbetonten Experiments

BACKGROUND: Inappropriate aldosterone and parathyroid hormone (PTH) secretion is associated with increased cardiovascular risk. Accumulating evidence suggests bidirectional interplay between aldosterone and PTH. METHODS: We evaluated the cross-sectional relationship between plasma aldosterone concentration (PAC), aldosterone to renin ratio (ARR) and PTH and subsequently tested whether the interaction between PAC and PTH modified the risk of cardiovascular death. PAC [78.0 (48.0-123.0) pg/mL], ARR [6.4 (2.9-12.9) pg/mL/pg/mL] and PTH concentration [median: 29.0 (22.0-40.0) pg/mL] were measured in 3074 patients (mean age: 62.5 ± 10.6 years; 30.3% women) referred to coronary angiography in a tertiary care center in Southwest Germany. RESULTS: Using multiple linear regression analysis, PAC and ARR emerged as an independent predictor of higher PTH concentrations (β=0.12 and 0.21, P<0.001 for both) irrespective of intake of antihypertensive treatment, 25(OH)D, kidney function, serum calcium, phosphate, magnesium, cortisol, NT-pro-BNP, soluble α-klotho and FGF-23 concentration. After a median follow-up of 9.9 years, 512 (16.7%) participants had died due to fatal cardiovascular events. Multivariate Cox proportional hazard analysis revealed that both PAC and PTH were independently associated with cardiovascular mortality, with a potential synergistic interaction (P=0.028). PAC and PTH are exclusively associated with cardiovascular death in subjects with PTH and PAC concentrations above the median, respectively (PAC: HR per log SD: 1.14; 95% CI 1.02-1.29; P=0.026; PTH: HR per log SD: 1.18; 95% CI 1.02-1.37; P=0.031). CONCLUSIONS: Higher PAC and ARR were independently associated with PTH. PAC was independently related to incident cardiovascular mortality exclusively in patients with elevated PTH and vice versa

A versatile strategy for the implementation of adaptive splines

This paper presents an implementation framework for spline spaces over T-meshes (and their d-dimensional analogs). The aim is to share code between the implementations of several spline spaces. This is achieved by reducing evaluation to a generalized Bézier extraction. The approach was tested by implementing hierarchical B-splines, truncated hierarchical B-splines, decoupled hierarchical B-splines (a novel variation presented here), truncated B-splines for partially nested refinement and hierarchical LR-splines