Numerical libraries have proven effective in providing widely reusable software that is robust, 
efficient, and scalable delivering advanced algorithms and data structures that enable scientific 
discovery for a broad range of applications. As we collectively address more advanced modeling, 
simulation, and analysis, the developers of open-source numerical libraries are increasingly encouraging 
community contributions to their software, and at the same time considering more effective strategies 
for connections with external packages that provide complementary functionality. We will discuss 
strategies for numerical library design and development that promote extensibility and community 
contributions. We will also discuss challenges and opportunities in working toward broader community 
scientific software ecosystems through the experience from the xSDK toolkit that integrates the four 
major open-source numerical libraries (hypre, SuperLU, PETSc, and Trilinos).