##### Imam Solekhudin, M.Si., Ph.D.

*Kepala Laboratorium Komputasi Matematika*

https://acadstaff.ugm.ac.id/MTk3OTAyMjAyMDAyMTIxMDAx

imams [at] ugm.ac.id

Computational mathematics offers methods of solving real problems numerically which uses numerical methods, such as Finite Difference Method, Finite Volume Method, Finite Element Methods, Boundary Element Methods, and Optimization Methods. The computational methods are implemented to simulated and real data.

This field is centred on the subject of inverse problems, which provide numerical solutions based on suitable numerical methods for mathematical models in many fields including the physical sciences, engineering and medical imaging. This subject is broad, ranging from the traditional numerical and more modern computational methods. The two aspects of the subject that we emphasize are computational differential equations and optimization methods.

Firstly, computational differential equations refer to the process of solving real world problems that governed by differential equations to achieve desired solutions, primarily through the use of numerical methods, such as Finite Difference Method, Finite Volume Method, Finite Element Methods, and Boundary Element Methods. Recent applications are implementation the methods on pollutant spread in the water, heat conduction and problems governed by diffusion-convection in layered-materials. Secondly, optimization methods deal with qualitative and quantitative analysis solutions of image reconstructions from under-sampled or incomplete data. The numerical methods have applications in diverse areas such as in medical particularly in tomography and industrial applications. Focus of the research is on iterative methods. A recent development is implementation of multi-resolution system such as wavelets and shearlets to improve the quality of the reconstructed images.

**Keywords:**

Finite Difference Method

Finite Volume Method

Finite Element Methods

Boundary Element Methods

Machine Learning

Heat Conduction

Pollutant Spread

Diffusion-Convection

Layered Materials

Inverse Problems

Bayesian inversion

Computed tomography

Computational inverse problems

Gaussian processes

Kalman filter

Wavelets

Shearlets