Dear colleagues and researchers,
The Journal of the Korean Society for Industrial and Applied Mathematics (J-KSIAM) Volume24 Number2 (June 2020 issue) has been posed on https://www.ksiam.org/archive or other information on the journal is available on the KSIAM website http://www.ksiam.org or https://www.ksiam.org/journal.
The journal is one of Korea Citation Indexed (KCI) journals since 2007 and is indexed in Emerging Sources Citation Index (ESCI) since 2017.
Readers interested in the following articles may download each of articles free of charge from our website and authors are encouraged to submit a paper via the online submission site.
Hi Jun Choe, Editor-in-Chief
Zhiming Chen, Hyeong-Ohk Bae, Tao Tang, Associate Editors-In-Chief
Jae Hoon Jung, Jaemyung Ahn, Wanho Lee, Managing Editors
THE STABILITY OF GAUGE-UZAWA METHOD TO SOLVE NANOFLUID
DEOK-KYU JANG, TAEK-CHEOL KIM, AND JAE-HONG PYO
Nanofluids is the fluids mixed with nanoscale particles and the mixed nano size materials affect heat transport. Researchers in this field has been focused on modeling and numerical computation by engineers In this paper, we analyze stability constraint of the dominant equations and check validate of the condition for most kinds of materials. So we mathematically analyze stability of the system. Also we apply Gauge-Uzawa algorithm to solve the system and prove stability of the method.
A CONSISTENT DISCONTINUOUS BUBBLE SCHEME FOR ELLIPTIC PROBLEMS WITH INTERFACE JUMPS
IN KWON AND GWANGHYUN JO
We propose a consistent numerical method for elliptic interface problems with nonhomogeneous jumps. We modify the discontinuous bubble immersed finite element method (DB-IFEM) introduced in (Chang et al. 2011), by adding a consistency term to the bilinear form. We prove optimal error estimates in L2 and energy like norm for this new scheme. One of the important technique in this proof is the Bramble-Hilbert type of interpolation error estimate for discontinuous functions. We believe this is a first time to deal with interpolation error estimate for discontinuous functions. Numerical examples with various interfaces are provided. We observe optimal convergence rates for all the examples, while the performance of early DB-IFEM deteriorates for some examples. Thus, the modification of the bilinear form is meaningful to enhance the performance.
RECENT ADVANCES IN DOMAIN DECOMPOSITION METHODS FOR TOTAL VARIATION MINIMIZATION
CHANG-OCK LEE AND JONGHO PARK
Total variation minimization is standard in mathematical imaging and there have been numerous researches over the last decades. In order to process large-scale images in real-time, it is essential to design parallel algorithms that utilize distributed memory computers efficiently. The aim of this paper is to illustrate recent advances of domain decomposition methods for total variation minimization as parallel algorithms. Domain decomposition methods are suitable for parallel computation since they solve a large-scale problem by dividing it into smaller problems and treating them in parallel, and they already have been widely used in structural mechanics. Differently from problems arising in structural mechanics, energy functionals of total variation minimization problems are in general nonlinear, nonsmooth, and nonseparable. Hence, designing efficient domain decomposition methods for total variation minimization is a quite challenging issue. We describe various existing approaches on domain decomposition methods for total variation minimization in a unified view. We address how the direction of research on the subject has changed over the past few years, and suggest several interesting topics for further research.
PARALLEL COMPUTATIONAL APPROACH FOR THREE-DIMENSIONAL SOLID ELEMENT USING EXTRA SHAPE FUNCTION BASED ON DOMAIN DECOMPOSITION APPROACH
HYUNSHIG JOO, DUHYUN GONG, SEUNG-HOON KANG, TAEYOUNG CHUN, AND SANG-JOON SHIN
This paper describes the development of a parallel computational algorithm based on the finite element tearing and interconnecting (FETI) method that uses a local Lagrange multiplier. In this approach, structural computational domain is decomposed into non-overlapping sub-domains using local Lagrange multiplier. The local Lagrange multipliers are imposed at interconnecting nodes. 8-node solid element using extra shape function is adopted by using the representative volume element (RVE). The parallel computational algorithm is further established based on message passing interface (MPI). Finally, the present FETI-local approach is implemented on parallel hardware and shows improved performance.
A LOCAL CONSERVATIVE MULTISCALE METHOD FOR ELLIPTIC PROBLEMS WITH OSCILLATING COEFFICIENTS
YOUNGMOK JEON AND EUN-JAE PARK
A new multiscale finite element method for elliptic problems with highly oscillating coefficients are introduced. A hybridization yields a locally flux-conserving numerical scheme for multiscale problems. Our approach naturally induces a homogenized equation which facilitates error analysis. Complete convergence analysis is given and numerical examples are presented to validate our analysis.
NONLOCAL FRACTIONAL DIFFERENTIAL INCLUSIONS WITH IMPULSE EFFECTS AND DELAY
NAWAL A. ALSARORI AND KIRTIWANT P. GHADLE
Functional fractional differential inclusions with impulse effects in general Banach spaces are studied. We discuss the situation when the semigroup generated by the linear part is equicontinuous and the multifunction is Caratheodory. First, we define the PC-mild solutions for functional fractional semilinear impulsive differential inclusions. We then prove the existence of PC-mild solutions for such inclusions by using the fixed point theorem, multivalued properties and applications of NCHM (noncompactness Hausdorff measure). Eventually, we enhance the acquired results by giving an example.