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"ppOpen-HPC" is an open source infrastructure for development and execution of optimized and reliable simulation code on post-peta-scale (pp) parallel computers based on many-core architectures, and it consists of various types of libraries, which cover general procedures for scientific computation. Source code developed on a PC with a single processor is linked with these libraries, and the parallel code generated is optimized for post-peta-scale systems with manycore architectures, such as the Oakforest-PACS system of Joint Center for Advanced High Performance Computing (JCAHPC). "ppOpen-HPC" is part of a five-year project (FY.2011-2015) spawned by the "Development of System Software Technologies for Post-Peta Scale High Performance Computing" funded by JST-CREST. The framework covers various types of procedures for scientific computations, such as parallel I/O of data-sets, matrix-assembly, linear-solvers with practical and scalable preconditioners, visualization, adaptive mesh refinement and dynamic load-balancing, in various types of computational models, such as FEM, FDM, FVM, BEM and DEM. Automatic tuning (AT) technology enables automatic generation of optimized libraries and applications under various types of environments. We release the most updated version of ppOpen-HPC as open source software every year in November (2012-2015), which is available at http://ppopenhpc.cc.u-tokyo.ac.jp/ppopenhpc/ . In 2016, the team of ppOpen-HPC joined ESSEX-II (Equipping Sparse Solvers for Exascale) project (Leading P.I. Professor Gerhard Wellein (University of Erlangen-Nuremberg)), which is funded by JST-CREST and the German DFG priority programme 1648 "Software for Exascale Computing" (SPPEXA) under Japan (JST)-Germany (DFG) collaboration until FY.2018. In ESSEX-II, we develop pK-Open-HPC (extended version of ppOpen-HPC, framework for exa-feasible applications), preconditioned iterative solvers for quantum sciences, and a framework for automatic tuning (AT) with performance model. In the presentation, various types of achievements of ppOpen-HPC, ESSEX-II, and pK-OpenHPC project, such as applications using HACApK library for H-matrix computation, coupling simulations by ppOpen-MATH/MP, and parallel preconditioned iterative solvers will be shown. Supercomputing in the Exa-scale and the Post-Moore Era is inherently different from that in the Peta-scale Era and before. Although supercomputers have been the essential tool for computational science in recent 30 years, they are now used for other purposes, such as data analytics, and machine learning. Architecture of the next generation supercomputing system is essentially heterogeneous for these multiple purposes (simulations + data + learning). We propose a new innovative method for integration of computational and data science (Big Data & Extreme Computing, BDEC) for sustainable promotion of new scientific discovery by supercomputers in the Exa-Scale/Post-Moore Era with heterogeneous architecture. "h3-Open-BDEC (h3: hierarchical, hybrid, heterogeneous,)" is an open source infrastructure for development and execution of optimized and reliable codes for BDEC on such supercomputers, which is the extended version of ppOpen-HPC. In this presentation, we will overview the h3-Open-BDEC, and the target supercomputer system, which will start operation in April 2021.