An implementation of a massively parallel domain decomposing direct finite element equation solver named FALKSOL is tested using the parallel version of the state of the art open-source solver MUMPS (MUltifrontal Massively Parallel Solver) as a reference. FALKSOL includes its own very advanced multi-level domain decomposition and load balancing procedure. In the elemental mode, MUMPS uses a single level domain decomposition, and then solves the interface problem. FALKSOL offers a full out-of-core functionality, while MUMPS offers only a partial one. The problem size that can be solved by MUMPS is therefore hard limited by the amount of physical memory plus swap space¹ present. This is an actual bottleneck. FALKSOL can solve much larger problems. It is essentially only limited by the size of the secondary storage available. With modern so-called Non-Volatile Memory express (NVMe) on the PCI bus, enough I/O bandwidth is obtained with a couple of raided units. The results show that MUMPS is about twice as fast as FALKSOL in the limited range of problem size it copes with. The solvers are complementary. The out-of-core multi-level domain decomposition algorithm in FALKSOL makes it scale. The test indicates that there is a considerable potential gain in scalability/elasticity choosing the FALKSOL multi-level domain-decomposition out-of-core approach. Especially considering more powerful and larger compute systems. The price to be paid in speed compared with MUMPS is reasonable. The current stand-alone implementation of FALKSOL is interfaced with the 3Dhp code Demkowicz (2007) [32], Demkowicz et al. (2008) [33]. The described MUMPS-like interface can be used to select the best solver for the task.

使用最先进的开源求解器 MUMPS（多正面大规模并行求解器）的并行版本作为参考，测试了名为 FALKSOL 的大规模并行域分解直接有限元方程求解器的实现。FALKSOL 包括其自己非常先进的多级域分解和负载平衡程序。在元素模式下，MUMPS 使用单级域分解，然后解决接口问题。FALKSOL 提供完整的核外功能，而 MUMPS 仅提供部分功能。MUMPS 可以解决的问题大小因此受到物理内存量加上交换空间^{1 的}硬限制展示。这是一个实际的瓶颈。FALKSOL 可以解决更大的问题。它基本上仅受可用辅助存储大小的限制。使用 PCI 总线上的现​​代所谓的非易失性存储器 (NVMe)，通过几个突袭单元可以获得足够的 I/O 带宽。结果表明，在其处理的问题规模有限的范围内，MUMPS 的速度大约是 FALKSOL 的两倍。求解器是互补的。FALKSOL 中的核外多级域分解算法使其可扩展。测试表明，选择 FALKSOL 多级域分解核外方法在可扩展性/弹性方面有相当大的潜在收益。特别是考虑到更强大和更大的计算系统。与 MUMPS 相比，在速度方面付出的代价是合理的。FALKSOL 当前的独立实现与 3Dhp 代码 Demkowicz (2007) [32]、Demkowicz 等人进行了接口。(2008) [33]。所描述的类似 MUMPS 的界面可用于为任务选择最佳求解器。