Structural mechanics is commonly modeled by (systems of) partial differential equations (PDEs). Except for very simple cases where analytical solutions exist, the use of numerical methods required to find approximate solutions. However, many problems practical interest, computational cost classical solvers running on classical, that is, silicon-based computer hardware, becomes prohibitive. Quantum computing, though still in its infancy, holds promise enabling a new generation algorithms can...

In this paper higher order mimetic discretizations are introduced which firmly rooted in the geometry variables defined. The shows how basic constructs differential have a discrete counterpart algebraic topology. Generic maps switch between continuous forms and cochains will be discussed finally realization of these ideas terms spectral elements is presented, based on projections for operations at finite dimensional level commute with level. two types orientation (inner- outer-orientation)...

CO2 sequestration and storage in deep saline aquifers is a promising technology for mitigating the excessive concentration of greenhouse gas atmosphere. However, accurately predicting migration plumes requires complex multi-physics-based numerical simulation approaches, which are prohibitively expensive due to highly nonlinear coupled governing equations uncertainties heterogeneous spatial parameter distributions. To address this challenge, we developed an end-to-end learning workflow...

Recent developments in Micro-Aerial Vehicles have stimulated research into insect aerodynamics. DNS studies of flight showed the important role vortex shedding on performance characteristics insects. Most airfoils considered where thick and had an unnatural, blunt (elliptic) trailing and/ or leading edge. Experimental results fixed also performing at sub-critical Reynolds numbers suggest a significant loss due to thickness edges, since they promote unfavorable separation boundary layer. In...

The numerical approximation of the mixed velocity-pressure-stress formulation Stokes problem using spectral methods is considered. In addition to compatibility condition between discrete velocity and pressure spaces, a second stress spaces must also be satisfied in order have well-posed problem. theory developed by considering doubly constrained minimization which viscous tensor minimized subject constraint that forces are irrotational. analyzed error estimates derived. A comparison approach...

In this paper I try to explain what one means when refers ’compatible’ or ’mimetic’ discretization methods. will show why approach is so appealing from a computational and physical point of view. respect, not really scientific paper, although some new ideas be presented, but – as the title suggests an introduction way looking at This papers shows path modeling, representation in terms differential forms, algebraic topological cochains with implementation orthogonal polynomials.

Abstract The quasilinear system of partial differential equations governing the flow a UCM fluid is known to be mixed elliptic‐hyperbolic type. compatibility associated with hyperbolic part are derived in this paper. There two characteristic variables that transported along characteristics. These both conditional well‐posedness system. case from constitutive equation alone. additional characteristics always present for unsteady inertial and which may steady flow. these involve coupling...

Given a sequence of finite element spaces which form de Rham sequence, we will construct dual representations these with associated differential operators connect such that they also sequence. The need to satisfy the on domain boundary. matrix converts primal – Hodge is mass or Gram matrix. It be shown bilinear and representation equal vector inner product expansion coefficients (degrees freedom) both representations. This leads very sparse system matrices, even for high order methods....