Numerical Parallel Scalability of the Shifted Boundary Method
Abstract
Many challenging problems in the engineering sciences are dominated by geometric complexity. Geometric complexity is often so overwhelming that the large majority of the design and analysis time is spent in the setup phase of the computation, that is, mesh generation and analogous tasks, such as geometry cleanup/healing. Presently, the PI is sponsored by the Mathematical Sciences Division of the Army Research Office (ARO) through a grant W911NF1810308 titled ÒThe shifted interface method for solid mechanics: An embedded domain approach.Ó In this sponsored research, the PI and his team at Duke University are developing embedded (or immersed) finite element numerical methods for solid mechanics applications, as a paradigm of computational mechanics applications. The PI and his research group have developed a new embedded finite element method, named Shifted Boundary Method (or SB method). This new approach overcomes the difficulty on matrix conditioning and algorithmic stability that the occurrence of small cut cells produced in standard embedded methods. This without creating complicated data structures and limiting in general computational complexity to a minimum. The key feature of the SB method is the idea of shifting the location where boundary conditions are applied from the true to the surrogate boundary, and to appropriately modify the shifted boundary conditions, enforced weakly, in order to preserve optimal convergence rates of the numerical solution. This process yields a method that is simple, robust, and efficient. These topics are the scope and goals of the ARO Grant W911NF1810308 mentioned above, in which embedded solid mechanics computational modeling of advancing interfaces is also pursued, as typical of growth/deposition processes involved in additive manufacturing. One aspect that is not the object of the work proposed in the ARO Grant W911NF1810308 is the analysis of performance of the SB method in the context of parallel computing architectures. It is expected from previous experience that the SB method should show good overall parallel scalability. In this proposal, the PI proposes to study the scalability of the SB method in an engineering application that could be relevant to the mission and vision of ARO in the realm of additive manufacturing and similar or related applications. The PI proposes to attack the problem of coupled thermo-elastoplasticity associated with the formation of residual stresses in 3Dprinted products during the cooling phase of the melting pool. This complex problem could be valuable as a representative test bed for the performance of the SB method in large-scale engineering simulations. For these reasons, the PI would like to request funding to build a relatively small computer cluster, but large enough to perform basic scalability tests. Work on this cluster should be intended as a first step in the development of algorithms whose performance will be validated on the large-scale computational platforms of the DOD. The outcomes of this proposal are expected to positively impact the outcomes of ARO Grant W911NF1810308, and to broaden its impact, both computationally and in terms of valuable engineering applications.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 09, 2020
- Source ID
- W911NF2010045
Entities
People
- Guglielmo Scovazzi
Organizations
- Army Contracting Command
- Duke University
- United States Army