The research topics of Prof. June-Yub Lee include numerical analysis, more specifically high-speed numerical methods based on the integral equations, and mathematical analysis of inverse problems using the high-speed methods. Among many research results, accelerating the non-uniform Fast Fourier Transform is a major research achievement that extends the FFT developed in 1965 and is one of the representative research achievements in the field of applied mathematics. The type3 NUFFT which extends the non-uniform Fourier transform technique, and MRI reconstruction technique using the NUFFT were studied. In addition, various studies on the inverse problem were conducted to develop the reconstruction formula, MREIT-related numerical technique, and the Equipotential method. And the polarization tensor and moment tensor methods that analyze the mathematical characteristics of the inverse problem were studied. Since 2014, research on the phase field equation such as the spectral method of the Allen-Cahn equation, the phase field crystal equation, the convex splitting RK method, and the 2nd order operator separation method are in progress. Recently, researches on scientific computation using artificial neural networks have been conducted.