An isogeometric finite element method for incompressible fluid film equations is presented. The method can be applied to numerically model the behaviour of thin cellular membranes, such as lipid bilayers. The membranes are represented by infinitely thin closed surfaces. Both the surface parametrization and analysis are based on state-of-the-art polar spline spaces. These spaces are defined such that a C1 continuous genus 0 surface can be constructed. At the discrete setting, point-wise conservation of mass is attained, using the framework of discrete exterior calculus. Therefore, the polar spline spaces are called divergence conforming. Time discretization of the highly non-linear system is done via the fixed-point iterations. It is found that for certain non-uniformly curved domains, the iterations converge and time stepping can be performed. However, for surfaces that are closely resembling a perfect sphere, the iterations are not stable for any ∆t. The solution is parameter-dependent and this indicates a possible bug in the Matlab code.

Solar energy is considered to be one of the most promising energy alternatives among many renewable energy sources. On the pathway towards achieving climate goals, dramatic scale up of clean technologies is required, however the installation of solar energy has the burden of intense land requirement. Therefore, the onset of floating solar technology can be the turning point to give incentive for more substantial deployment of solar energy, avoiding land occupancy concerns. Besides the potential of installing bodies on water, floating solar brings the benefit of an efficiency increase superior to 10 percent in relation to land based solar, depending on the solar panel technology and environmental conditions. This efficiency increase can be attributed to the natural cooling effect of the seawater, located below the solar platform.