Asynchronous Stabilisation and Assembly Techniques for Additive Multigrid

Multigrid solvers are among the best solvers in the world, but once applied in the real world there are issues they must overcome. Many multigrid phases exhibit low concurrency. Mesh and matrix assembly are challenging to parallelise and introduce algorithmic latency. Dynamically adaptive codes exacerbate these issues. Multigrid codes require the computation of a cascade of matrices and dynamic adaptivity means these matrices are recomputed throughout the solve. Existing methods to compute the matrices are expensive and delay the solve. Non- trivial material parameters further increase the cost of accurate equation integration. We propose to assemble all matrix equations as stencils in a delayed element-wise fashion. Early multigrid iterations use cheap geometric approximations and more accurate updated stencil integrations are computed in parallel with the multigrid cycles. New stencil integrations are evaluated lazily and asynchronously fed to the solver once they become available. They do not delay multigrid iterations. We deploy stencil integrations as parallel tasks that are picked up by cores that would otherwise be idle. Coarse grid solves in multiplicative multigrid also exhibit limited concurrency. Small coarse mesh sizes correspond to small computational workload and require costly synchronisation steps. This acts as a bottleneck and delays solver iterations. Additive multigrid avoids this restriction, but becomes unstable for non-trivial material parameters as additive coarse grid levels tend to overcorrect. This leads to oscillations. We propose a new additive variant, adAFAC-x, with a stabilisation parameter that damps coarse grid corrections to remove oscillations. Per-level we solve an additional equation that produces an auxiliary correction. The auxiliary correction can be computed additively to the rest of the solve and uses ideas similar to smoothed aggregation multigrid to anticipate overcorrections. Pipelining techniques allow adAFAC-x to be written using single-touch semantics on a dynamically adaptive mesh

Task allocation in group of nodes in the IoT: A consensus approach

The realization of the Internet of Things (IoT) paradigm relies on the implementation of systems of cooperative intelligent objects with key interoperability capabilities. In order for objects to dynamically cooperate to IoT applications' execution, they need to make their resources available in a flexible way. However, available resources such as electrical energy, memory, processing, and object capability to perform a given task, are often limited. Therefore, resource allocation that ensures the fulfilment of network requirements is a critical challenge. In this paper, we propose a distributed optimization protocol based on consensus algorithm, to solve the problem of resource allocation and management in IoT heterogeneous networks. The proposed protocol is robust against links or nodes failures, so it's adaptive in dynamic scenarios where the network topology changes in runtime. We consider an IoT scenario where nodes involved in the same IoT task need to adjust their task frequency and buffer occupancy. We demonstrate that, using the proposed protocol, the network converges to a solution where resources are homogeneously allocated among nodes. Performance evaluation of experiments in simulation mode and in real scenarios show that the algorithm converges with a percentage error of about±5% with respect to the optimal allocation obtainable with a centralized approach

An asynchronous method for cloud-based rendering

Interactive high-fidelity rendering is still unachievable on many consumer devices. Cloud gaming services have shown promise in delivering interactive graphics beyond the individual capabilities of user devices. However, a number of shortcomings are manifest in these systems: high network bandwidths are required for higher resolutions and input lag due to network fluctuations heavily disrupts user experience. In this paper, we present a scalable solution for interactive high-fidelity graphics based on a distributed rendering pipeline where direct lighting is computed on the client device and indirect lighting in the cloud. The client device keeps a local cache for indirect lighting which is asynchronously updated using an object space representation; this allows us to achieve interactive rates that are unconstrained by network performance for a wide range of display resolutions that are also robust to input lag. Furthermore, in multi-user environments, the computation of indirect lighting is amortised over participating clients