We present an algebraic multigrid (AMG) method for the efficient solution of linear (block-)systems stemming from a discretization of a system of partial differential equations (PDEs). It generalizes the classical AMG approach for scalar problems to systems of PDEs in a natural blockwise fashion. We apply this approach to linear elasticity and show that the block-interpolation, described in thi...

In 2004 Kim and Chan performed a torsional oscillator measurement of the rotational inertia of solid helium-4. They found frequency changes which were interpreted in terms of a non-classical rotational inertia, that is a partial superfluidity or “supersolidity” of solid helium-4. Since then there have been many further studies using various versions of this technique. One important question tha...

An energy-based, phase field model is developed for the coupling of two incompressible, immiscible complex fluid phases, in particular a nematic liquid crystal phase in a viscous fluid phase. The model consists of a system of coupled nonlinear partial differential equations for conservation of mass and momentum, phase transport, and interfacial boundary conditions. An efficient and easy-to-impl...

and objectives In tutorial 2, we demonstrated the basic steps for deriving the direct boundary integral equation. In this tutorial we will explain, with more examples, the derivation of the direct boundary integral equation for systems of partial differential equations. We will consider two examples: elasticity problems and shear-deformable plate bending problems. 1 Elasticity equations In this...

Magnetic resonance elastography (MRE) noninvasively images the propagation of mechanical waves within soft tissues. The elastic properties of soft tissues can then be quantified from MRE wave snapshots. Various algorithms have been proposed to obtain their inversion for soft tissue elasticity. Anomalies are assumed to be discernible in the elasticity map. We propose a new elastic level set mode...

The present study focuses on the utilization of Sugarcane Bagasse Ash as replacement material for cement in concrete production. Sugarcane Bagasse ash contains high amorphous silica content and aluminium ion. For experimental investigations, Sugarcane bagasse ash and its chemical properties are obtained from KCP sugar factory, Andhra Pradesh. Ordinary Portland cement was partly replaced by suga...