We present DIQ-MPM, a novel monolithic two-way coupling framework for simulating interactions between solids modeled with the total Lagrangian formulation and Eulerian incompressible fluids using the Material Point Method (MPM). Our approach combines an implicit TLMPM formulation with a mixed velocity-pressure scheme to robustly simulate compressible solids undergoing large deformations, while eliminating numerical fractures. To enable strong fluid-solid coupling without relying on overlapping grids, we introduce a Dual Interface Quadrature (DIQ) mechanism that maps fluid-solid interface information consistently between the current and reference configurations. This allows us to construct a unified sparse pressure-only system via Schur complement, leading to efficient and stable coupling. We also integrate a particle-based contact force model to resolve solid-solid and solid-boundary contacts within implicit TLMPM. Experimental results demonstrate that our method stably captures free-slip coupling, large deformation phenomena, and complex interactions between compressible solids and incompressible fluids.

In edge computing, offloading complex computation tasks from terminals to nearby edge nodes (ENs) is a critical solution. When an EN cannot complete the tasks independently, it offloads partial tasks to other ENs. These ENs return the results to the original EN, which integrates them before sending the final output to the terminal. This process, called cooperative task offloading, introduces significant security challenges, especially since ENs are typically provided by third parties. Some ENs, driven by self-interest or vulnerability to attack, may provide incorrect results to other ENs (i.e., acting as malicious ENs), ultimately causing the terminal to receive incorrect results. While existing schemes can help terminals detect incorrect results, they fail to locate the malicious ENs, leaving the system in an unreliable state and causing invalid computations based on erroneous intermediate results. We propose a reputation-driven gradual verification scheme (RDGV) to identify and locate malicious ENs. In RDGV, each EN is held accountable for the correctness of its results and faces penalties if the results are found to be incorrect. Successor ENs must verify the intermediate results before utilizing them. That is, gradual verification. An economic incentive rule counters potential attacks from malicious ENs, while reputation, representing EN’s trustworthiness, guides a personalized verification strategy to reduce overall verification overhead. The effectiveness and advantages of RDGV are shown by simulation results and comparison with related work. The findings indicate that honest and continuous service is the optimal strategy for ENs to maintain the credibility of the edge system.